Relevant bibliographies by topics / Density eigenvalue

Academic literature on the topic 'Density eigenvalue'

Author: Grafiati
Published: 14 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Density eigenvalue.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Density eigenvalue"

1

Fyodorov, Yan V., Boris A. Khoruzhenko, and Mihail Poplavskyi. "Extreme Eigenvalues and the Emerging Outlier in Rank-One Non-Hermitian Deformations of the Gaussian Unitary Ensemble." Entropy 25, no. 1 (December 30, 2022): 74. http://dx.doi.org/10.3390/e25010074.

Full text
Abstract:
Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N≫1 the eigenvalue density of J undergoes an abrupt restructuring at γ=1, the critical threshold beyond which a single eigenvalue outlier (“broad resonance”) appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold γ=1 and the associated scaling for the real parts (“resonance positions”) and imaginary parts (“resonance widths”) of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function.
APA, Harvard, Vancouver, ISO, and other styles
2

Chen, Lung-Hui. "On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/3838507.

Full text
Abstract:
We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative ∂rΔx^=(1+nrx^)/π.
APA, Harvard, Vancouver, ISO, and other styles
3

Christandl, Matthias, Brent Doran, Stavros Kousidis, and Michael Walter. "Eigenvalue Distributions of Reduced Density Matrices." Communications in Mathematical Physics 332, no. 1 (August 19, 2014): 1–52. http://dx.doi.org/10.1007/s00220-014-2144-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Wu, Na, Ke Wang, Liangtian Wan, and Ning Liu. "A Source Number Estimation Algorithm Based on Data Local Density and Fuzzy C-Means Clustering." Wireless Communications and Mobile Computing 2021 (February 20, 2021): 1–7. http://dx.doi.org/10.1155/2021/6658785.

Full text
Abstract:
An advanced source number estimation (SNE) algorithm based on both fuzzy C-means clustering (FCM) and data local density (DLD) is proposed in this paper. The DLD of an eigenvalue refers to the number of eigenvalues within a specific neighborhood of this eigenvalue belonging to the data covariance matrix. This local density essentially as the one-dimensional sample feature of the FCM is extracted into the SNE algorithm based on FCM and can enable to improve the probability of correct detection (PCD) of the SNE algorithm based on the FCM especially for low signal-to-noise ratio (SNR) environment. Comparison experiment results demonstrate that compared to the SNE algorithm based on the FCM and other similar algorithms, our proposed algorithm can achieve highest PCD of the incident source number in both cases of spatial white noise and spatial correlation noise.
APA, Harvard, Vancouver, ISO, and other styles
5

CASTRO, C., and E. ZUAZUA. "High frequency asymptotic analysis of a string with rapidly oscillating density." European Journal of Applied Mathematics 11, no. 6 (December 2000): 595–622. http://dx.doi.org/10.1017/s0956792500004307.

Full text
Abstract:
We consider the eigenvalue problem associated with the vibrations of a string with rapidly oscillating periodic density. In a previous paper we stated asymptotic formulae for the eigenvalues and eigenfunctions when the size of the microstructure ε is shorter than the wavelength of the eigenfunctions 1/√λε. On the other hand, it has been observed that when the size of the microstructure is of the order of the wavelength of the eigenfunctions (ε ∼ 1/√λε) singular phenomena may occur. In this paper we study the behaviour of the eigenvalues and eigenfunctions when 1/√λε is larger than the critical size ε. We use the WKB approximation which allows us to find an explicit formula for eigenvalues and eigenfunctions with respect to ε. Our analysis provides all order correction formulae for the limit eigenvalues and eigenfunctions above the critical size. Each term of the asymptotic expansion requires one more derivative of the density. Thus, a full description requires the density to be C∞ smooth.
APA, Harvard, Vancouver, ISO, and other styles
6

SaiToh, Akira, Roabeh Rahimi, and Mikio Nakahara. "Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation." Quantum Information and Computation 12, no. 11&12 (November 2012): 944–52. http://dx.doi.org/10.26421/qic12.11-12-3.

Full text
Abstract:
Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord implies the existence of nonclassical correlation. It is known that only the matrix transposition is nontrivial among Hermiticity-preserving (HP) linear EnCE maps when we use the changes in the eigenvalues of a density matrix due to a partial map for the purpose. In this paper, we prove that this is true even among not-necessarily HP (nnHP) linear EnCE maps. The proof utilizes a conventional theorem on linear preservers. This result imposes a strong limitation on the linear maps and promotes the importance of nonlinear maps.
APA, Harvard, Vancouver, ISO, and other styles
7

Frank, Olaf, and Bruno Eckhardt. "Eigenvalue density oscillations in separable microwave resonators." Physical Review E 53, no. 4 (April 1, 1996): 4166–75. http://dx.doi.org/10.1103/physreve.53.4166.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Menon, Ravishankar, Peter Gerstoft, and William S. Hodgkiss. "Asymptotic Eigenvalue Density of Noise Covariance Matrices." IEEE Transactions on Signal Processing 60, no. 7 (July 2012): 3415–24. http://dx.doi.org/10.1109/tsp.2012.2193573.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

He, Yukun, and Antti Knowles. "Mesoscopic eigenvalue density correlations of Wigner matrices." Probability Theory and Related Fields 177, no. 1-2 (October 4, 2019): 147–216. http://dx.doi.org/10.1007/s00440-019-00946-w.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Erdős, László, and Brendan Farrell. "Local Eigenvalue Density for General MANOVA Matrices." Journal of Statistical Physics 152, no. 6 (July 18, 2013): 1003–32. http://dx.doi.org/10.1007/s10955-013-0807-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Density eigenvalue"

1

ABRATE, NICOLO'. "Methods for safety and stability analysis of nuclear systems." Doctoral thesis, Politecnico di Torino, 2022. http://hdl.handle.net/11583/2971611.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Adhikari, Dikshya. "The Role of Eigenvalues of Parity Check Matrix in Low-Density Parity Check Codes." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707297/.

Full text
Abstract:
The new developments in coding theory research have revolutionized the application of coding to practical systems. Low-Density Parity Check (LDPC) codes form a class of Shannon limit approaching codes opted for digital communication systems that require high reliability. This thesis investigates the underlying relationship between the spectral properties of the parity check matrix and LDPC decoding convergence. The bit error rate of an LDPC code is plotted for the parity check matrix that has different Second Smallest Eigenvalue Modulus (SSEM) of its corresponding Laplacian matrix. It is found that for a given (n,k) LDPC code, large SSEM has better error floor performance than low SSEM. The value of SSEM decreases as the sparseness in a parity-check matrix is increased. It was also found from the simulation that long LDPC codes have better error floor performance than short codes. This thesis outlines an approach to analyze LDPC decoding based on the eigenvalue analysis of the corresponding parity check matrix.
APA, Harvard, Vancouver, ISO, and other styles
3

Kharate, Neha Ashok. "A Convergence Analysis of LDPC Decoding Based on Eigenvalues." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011778/.

Full text
Abstract:
Low-density parity check (LDPC) codes are very popular among error correction codes because of their high-performance capacity. Numerous investigations have been carried out to analyze the performance and simplify the implementation of LDPC codes. Relatively slow convergence of iterative decoding algorithm affects the performance of LDPC codes. Faster convergence can be achieved by reducing the number of iterations during the decoding process. In this thesis, a new approach for faster convergence is suggested by choosing a systematic parity check matrix that yields lowest Second Smallest Eigenvalue Modulus (SSEM) of its corresponding Laplacian matrix. MATLAB simulations are used to study the impact of eigenvalues on the number of iterations of the LDPC decoder. It is found that for a given (n, k) LDPC code, a parity check matrix with lowest SSEM converges quickly as compared to the parity check matrix with high SSEM. In other words, a densely connected graph that represents the parity check matrix takes more iterations to converge than a sparsely connected graph.
APA, Harvard, Vancouver, ISO, and other styles
4

Berglund, Filip. "Asymptotics of beta-Hermite Ensembles." Thesis, Linköpings universitet, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-171096.

Full text
Abstract:
In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). Specifically we look at the empirical distribution function and two different scalings of the largest eigenvalue. The results we present relating to these statistics are the convergence of the empirical distribution function to the semicircle law, the convergence of the scaled largest eigenvalue to the Tracy-Widom distributions, and with a different scaling, the convergence of the largest eigenvalue to 1. We also use simulations to illustrate these results. For the Gaussian unitary ensemble, we present an expression for its level density. To aid in understanding the Gaussian symplectic ensemble we present properties of the eigenvalues of quaternionic matrices. Finally, we prove a theorem about the symmetry of the order statistic of the eigenvalues of the beta-Hermite ensembles.
I denna kandidatuppsats presenterar vi resultat om några olika egenvärdens-statistikor från beta-Hermite ensemblerna, först i de klassiska fallen då beta = 1, 2, 4, det vill säga den gaussiska ortogonala ensemblen (bestående av reella symmetriska matriser), den gaussiska unitära ensemblen (bestående av komplexa hermitiska matriser) och den gaussiska symplektiska ensemblen (bestående av kvaternioniska själv-duala matriser). Vi tittar även på de mindre undersökta generella beta-Hermite ensemblerna (bestående av reella symmetriska tridiagonala matriser). Specifikt tittar vi på den empiriska fördelningsfunktionen och två olika normeringar av det största egenvärdet. De resultat vi presenterar för dessa statistikor är den empiriska fördelningsfunktionens konvergens mot halvcirkel-fördelningen, det normerade största egenvärdets konvergens mot Tracy-Widom fördelningen, och, med en annan normering, största egenvärdets konvergens mot 1. Vi illustrerar även dessa resultat med hjälp av simuleringar. För den gaussiska unitära ensemblen presenterar vi ett uttryck för dess nivåtäthet. För att underlätta förståelsen av den gaussiska symplektiska ensemblen presenterar vi egenskaper hos egenvärdena av kvaternioniska matriser. Slutligen bevisar vi en sats om symmetrin hos ordningsstatistikan av egenvärdena av beta-Hermite ensemblerna.
APA, Harvard, Vancouver, ISO, and other styles
5

Michaïl, Alkéos. "Eigenvalues and eigenvectors of large matrices under random perturbations." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCB214.

Full text
Abstract:
La présente thèse est consacrée à l’étude de l’effet d’une perturbation sur le spectre d’une matrice hermitienne perturbée par une matrice aléatoire de petite norme opérateur et dont les entrées dans la base propre de la première matrice sont indépendantes, centrées et possèdent un profil de variance. Ceci est réalisé au travers de développements perturbatifs de divers types des lois spectrales des grandes matrices perturbées considérées. Dans un premier temps, nous démontrons différents développements perturbatifs de la mesure spectrale empirique dans les cas du régime perturbatif et du régime semi-perturbatif et mettons en évidence des modèles heuristiques bien connus en physique, comme la transition entre les régimes semi-perturbatifs et perturbatifs. Dans un deuxième temps, nous proposons une étude approfondie du régime semi-perturbatif et prouvons le fait nouveau que ce régime peut être décomposé en un nombre infini de sous-régimes. Enfin, nous démontrons, au travers d’un développement perturbatif des mesures spectrales associées à un vecteur donné, un développement perturbatif des coordonnées des vecteurs propres des matrices perturbées que nous considérons
The present thesis is devoted to the study of the effect of a perturbation on the spectrum of a Hermitian matrix by a random matrix with small operator norm and whose entries in the eigenvector basis of the first one were independent, centered and with a variance profile. This is carried out through perturbative expansions of various types of spectral laws of the considered perturbed large matrices. First, we demonstrate different perturbative expansions of the empirical spectral measure in the cases of the perturbative regime and the semi-perturbative regime and highlight well known heuristic patterns in Physics, as the transition between semi-perturbative and perturbative regimes. Secondly, we provide a thorough study of the semi-perturbative regime and prove the new fact that this regime could be decomposed into infinitely many sub-regimes. Finally, we prove, through a perturbative expansion of spectral measures associated to the state defined by a given vector, a perturbative expansion of the coordinates of the eigenvectors of the perturbed matrices
APA, Harvard, Vancouver, ISO, and other styles
6

Sushma, Kumari. "Topics in random matrices and statistical machine learning." Kyoto University, 2018. http://hdl.handle.net/2433/235047.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Quarcoo, Joseph. "Contributions to the degree theory for perturbation of maximal monotone maps." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001654.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Provenzano, Luigi. "On mass distribution and concentration phenomena for linear elliptic partial differential operators." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424499.

Full text
Abstract:
In this thesis we study the dependence of the eigenvalues of elliptic partial differential operators upon mass density perturbations on open subsets of the N-dimensional euclidean space. We prove continuity and analyticity results for the eigenvalues of poly-harmonic operators and apply them to certain optimization problems. In order to prove analyticity, we use a general technique of P.D. Lamberti and M. Lanza de Cristoforis, and we obtain formulas for the Frechet differentials of the eigenvalues which are used to characterize critical mass densities under the constraint that the total mass is preserved. Then we state a sort of `maximum principle' in spectral optimization problems for elliptic operators subject to mass density perturbations. Moreover, we consider a special class of densities, namely densities which concentrate near the boundary of open subsets of the N-dimensional euclidean space. We study the asymptotic behavior of the eigenvalues of Neumann-type problems for the Laplace and the biharmonic operator. By adapting a general technique of J.M. Arrieta, we prove that the Neumann eigenvalues converge to the appropriate limiting Steklov eigenvalues. In this way, we formulate a genuine Steklov eigenvalue problem for the biharmonic operator. In the case of the Laplace operator we prove the validity of an asymptotic expansion of the Neumann eigenvalues and eigenfunctions and provide formulas for the first terms in the expansions. We adapt to our case asymptotic analysis techniques used by M.E. Perez and S.A. Nazarov to describe vibrating systems with masses concentrated at points or along curves. Moreover, we consider the problem of domain perturbations for the biharmonic Steklov problem obtained with this mass concentration procedure and prove that balls are critical domains for all the eigenvalues. Then we adapt the arguments of F. Brock and R. Weinstock to prove that the ball is actually a maximizer for the rst positive eigenvalue among bounded domains of given measure. Moreover, we provide a quantitative version of such an isoperimetric inequality, showing also that it is sharp.
In questa tesi studiamo la dipendenza degli autovalori di operatori differenziali alle derivate parziali di tipo ellittico da perturbazioni della densità di massa su aperti dello spazio euclideo N-dimensionale. In particolare, proviamo risultati di dipendenza continua e analitica degli autovalori di operatori poliarmonici e li applichiamo ad alcuni problemi di ottimizzazione. Per provare i risultati di analiticità, adoperiamo una tecnica generale sviluppata da P.D. Lamberti e M. Lanza de Cristoforis, ottenendo formule per i differenziali di Frechet degli autovalori che ci permettono di caratterizzare le densità critiche sotto il vincolo di massa fissata. Inoltre, enunciamo un `principio di massimo' per la classe di problemi di ottimizzazione considerata. In seguito, prendiamo in esame una famiglia particolare di densità di massa, ovvero densità che si concentrano al bordo degli aperti dove i problemi differenziali sono definiti. In questo caso, studiamo il comportamento asintotico degli autovalori e delle autofunzioni dei problemi di Neumann per l'operatore di Laplace e l'operatore biarmonico quando la massa si concentra al bordo. Proviamo in entrambi i casi, adattando una tecnica generale sviluppata da J.M. Arrieta, che gli autovalori e le autofunzioni del problema di Neumann convergono agli autovalori e alle autofunzioni di appropriati problemi limite di tipo Steklov. In particolare, il problema di tipo Steklov per l'operatore biarmonico così formulato viene introdotto per la prima volta in questa tesi, dove ne vengono poi studiate alcune proprietà. Nel caso dell'operatore di Laplace, proviamo la validità di un'espansione asintotica degli autovalori e delle autofunzioni del problema di Neumann fino al primo ordine ed otteniamo formule esplicite per i primi termini delle espansioni. Per ottenere questi risultati adattiamo al nostro problema delle tecniche di analisi asintotica utilizzate da M.E. Perez e S.A. Nazarov per lo studio di sistemi vibranti con masse concentrate in punti o lungo certe curve. Per quanto riguarda il problema di Steklov per l'operatore biarmonico, consideriamo anche il problema della dipendenza degli autovalori dal dominio. Utilizzando sempre la tecnica generale sviluppata da P.D. Lamberti e M. Lanza de Cristoforis, proviamo che le palle sono domini critici per tutti gli autovalori. Inoltre, adattando l'argomento di F. Brock e R.Weinstock per il problema di Steklov per l'operatore di Laplace, riusciamo a mostrare che la palla massimizza il primo autovalore positivo del problema di Steklov per l'operatore biarmonico tra tutti gli aperti limitati di misura fissata. Proviamo infine una versione quantitativa di questa disuguaglianza isoperimetrica, mostrando poi che l'esponente che compare nella disuguaglianza è ottimale.
APA, Harvard, Vancouver, ISO, and other styles
9

Rubensson, Emanuel H. "Matrix Algebra for Quantum Chemistry." Doctoral thesis, Stockholm : Bioteknologi, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9447.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Sbai, Youssef. "Analyse semi-classique des opérateurs périodiques perturbés." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0270/document.

Full text
Abstract:
Cette thèse traite de certaines propriétés spectrales de deux classes spécifiques des opérateurs périodiques. Nous nous intéressons tout d’abord à un modèle périodique perturbée par un opérateur dépendant d’un petit paramètre semi-classique. Nous obtenons alors le comportement asymptotique de la fonction du comptage des valeurs propres dans les gaps spectrales avec une estimation optimale du reste. Le second modèle étudié dans cette thèse est un modèle elliptique périodique d’ordre deux perturbée par un opérateur dépendant d’une grande constante de couplage. Nous donnons également la description de la fonction de compactage des valeurs propres lorsque la constante de couplage tend vers l’infini. La dernière partie de cette thèse discute l’étude du spectre discret de l’opérateur de Schrödinger avec un potentiel très oscillent dépendant d’un petit paramètre semi-classique
This Ph.D thesis deals with some spectral properties of two specific classes of two periodic operators. We are firstly interested in the model periodic perturbed by operator depending on a small semi-classical constant. We obtain an asymptotic behavior of the eigenvalue counting function in the spectral gaps with scharp remainder estimate. The second model studied in this thesis is a two-dimensional periodic elliptic second order opera-tor perturbed by operator depending on a large coupling constant. We also give the description of the counting function of eigenvalues when the coupling constant tends to infinity. The last part of this thesis highlights the study the spectrum of a Schrödinger operator perturbed by a fast oscillatingdecaying potential depending on a small parameter
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Density eigenvalue"

1

Beenakker, Carlo W. J. Extreme eigenvalues of Wishart matrices: application to entangled bipartite system. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.37.

Full text
Abstract:
This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.
APA, Harvard, Vancouver, ISO, and other styles
2

Brezin, Edouard, and Sinobu Hikami. Beta ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.20.

Full text
Abstract:
This article deals with beta ensembles. Classical random matrix ensembles contain a parameter β, taking on the values 1, 2, and 4. This parameter, which relates to the underlying symmetry, appears as a repulsion sβ between neighbouring eigenvalues for small s. β may be regarded as a continuous positive parameter on the basis of different viewpoints of the eigenvalue probability density function for the classical random matrix ensembles - as the Boltzmann factor for a log-gas or the squared ground state wave function of a quantum many-body system. The article first considers log-gas systems before discussing the Fokker-Planck equation and the Calogero-Sutherland system. It then describes the random matrix realization of the β-generalization of the circular ensemble and concludes with an analysis of stochastic differential equations resulting from the case of the bulk scaling limit of the β-generalization of the Gaussian ensemble.
APA, Harvard, Vancouver, ISO, and other styles
3

Akemann, Gernot. Random matrix theory and quantum chromodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0005.

Full text
Abstract:
This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.
APA, Harvard, Vancouver, ISO, and other styles
4

Speicher, Roland. Random banded and sparse matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.23.

Full text
Abstract:
This article discusses some mathematical results and conjectures about random band matrix ensembles (RBM) and sparse matrix ensembles. Spectral problems of RBM and sparse matrices can be expressed in terms of supersymmetric (SUSY) statistical mechanics that provides a dual representation for disordered quantum systems. This representation offers important insights into nonperturbative aspects of the spectrum and eigenfunctions of RBM. The article first presents the definition of RBM ensembles before considering the density of states, the behaviour of eigenvectors, and eigenvalue statistics for RBM and sparse random matrices. In particular, it highlights the relations with random Schrödinger (RS) and the role of the dimension of the lattice. It also describes the connection between RBM and statistical mechanics, the spectral theory of large random sparse matrices, conjectures and theorems about eigenvectors and local spacing statistics, and the RS operator on the Cayley tree or Bethe lattice.
APA, Harvard, Vancouver, ISO, and other styles
5

Zabrodin, Anton. Financial applications of random matrix theory: a short review. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.40.

Full text
Abstract:
This article reviews some applications of random matrix theory (RMT) in the context of financial markets and econometric models, with emphasis on various theoretical results (for example, the Marčenko-Pastur spectrum and its various generalizations, random singular value decomposition, free matrices, largest eigenvalue statistics) as well as some concrete applications to portfolio optimization and out-of-sample risk estimation. The discussion begins with an overview of principal component analysis (PCA) of the correlation matrix, followed by an analysis of return statistics and portfolio theory. In particular, the article considers single asset returns, multivariate distribution of returns, risk and portfolio theory, and nonequal time correlations and more general rectangular correlation matrices. It also presents several RMT results on the bulk density of states that can be obtained using the concept of matrix freeness before concluding with a description of empirical correlation matrices of stock returns.
APA, Harvard, Vancouver, ISO, and other styles
6

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

Full text
Abstract:
This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.
APA, Harvard, Vancouver, ISO, and other styles
7

Guhr, Thomas. Replica approach in random matrix theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.8.

Full text
Abstract:
This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Density eigenvalue"

1

Sjöstrand, Johannes, and Martin Vogel. "Interior Eigenvalue Density of Jordan Matrices with Random Perturbations." In Trends in Mathematics, 439–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52471-9_24.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Adhikari, S., and L. A. Pastur. "Extremely strong convergence of eigenvalue-density of linear stochastic dynamical systems." In IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties, 331–45. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0289-9_24.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Muhumuza, Asaph Keikara, Karl Lundengård, Jonas Österberg, Sergei Silvestrov, John Magero Mango, and Godwin Kakuba. "Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant." In Springer Proceedings in Mathematics & Statistics, 819–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41850-2_34.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Yamada, Susumu, Masahiko Okumura, and Masahiko Machida. "High Performance Computing for Eigenvalue Solver in Density-Matrix Renormalization Group Method: Parallelization of the Hamiltonian Matrix-Vector Multiplication." In High Performance Computing for Computational Science - VECPAR 2008, 39–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-92859-1_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Umrigar, C. J., A. Savin, and Xavier Gonze. "Are Unoccupied Kohn-Sham Eigenvalues Related to Excitation Energies?" In Electronic Density Functional Theory, 167–76. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0316-7_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Engel, G. E., and Warren E. Pickett. "Density Functionals for Energies and Eigenvalues: Local Mass Approximation." In Electronic Density Functional Theory, 299–309. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0316-7_21.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Girko, Vyacheslav L. "Class of Canonical V-Equations K 26 for a Single Matrix and a Product of Two Random Matrices. The V-Density of Eigenvalues of Random Matrices such that the Variances of their Entries Form a Doubly Stochastic Matrix." In Theory of Stochastic Canonical Equations, 383–400. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_26.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

"Eigenvalue density." In A Dynamical Approach to Random Matrix Theory, 11–16. Providence, Rhode Island: American Mathematical Society, 2017. http://dx.doi.org/10.1090/cln/028/03.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Arif, Omar, and Patricio A. "Robust Density Comparison Using Eigenvalue Decomposition." In Principal Component Analysis. InTech, 2012. http://dx.doi.org/10.5772/38517.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Nesterov, Sergei. "Free Vibrations of a Rectangular Membrane with Sharply Varying Surface Density." In High-Precision Methods in Eigenvalue Problems and Their Applications, 201–13. Chapman and Hall/CRC, 2004. http://dx.doi.org/10.1201/9780203401286.ch14.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Density eigenvalue"

1

Osborn, James C., and Tilo Wettig. "Dirac eigenvalue correlations in quenched QCD at finite density." In XXIIIrd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2005. http://dx.doi.org/10.22323/1.020.0200.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Wang, B., C. Lu, and R. Yang. "Optimal topology for maximum eigenvalue using density-dependent material model." In 37th Structure, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-1627.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Kodrasi, Ina, and Simon Doclo. "Late reverberant power spectral density estimation based on an eigenvalue decomposition." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7952228.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Schaefer, D., A. Lauer, and R. Baggen. "Characterization of noisy EM fields by cross spectral density eigenvalue analysis." In 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2017. http://dx.doi.org/10.1109/iceaa.2017.8065400.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Lawson, Anthony L., and Ramkumar N. Parthasarathy. "Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected Into a High-Density Gas." In ASME 2002 Engineering Technology Conference on Energy. ASMEDC, 2002. http://dx.doi.org/10.1115/etce2002/cae-29010.

Full text
Abstract:
It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.
APA, Harvard, Vancouver, ISO, and other styles
6

Xie, Zhe, Yangwei Liu, Xiaohua Liu, Lipeng Lu, and Xiaofeng Sun. "Effect of RANS Method on Stall Inception Eigenvalue Approach." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64708.

Full text
Abstract:
The effect of mesh, turbulence model and discretization scheme in Reynolds-averaged Navier-Stokes method (RANS) on a stall inception eigenvalue approach is investigated in a transonic compressor rotor. The most influencing flow structures on the result of eigenvalue approach are also identified. The compressor stall point is calculated by a recently developed eigenvalue model. Based on the 3D Navier-Stokes equations, the body-force term and small disturbance were used to transform the original equations into the eigenvalue approach. Because the eigenvalue mainly relies on the results from RANS, the sensitivity of the eigenvalue to the mesh density, turbulence model, and numerical scheme needs to be clearly identified before it is applied to engineering. The effect of mesh density is firstly specified. Several grids with different densities and distributions are employed in RANS. The eigenvalue results indicate that the solution converges at the same grid density as RANS does. Besides, the eigenvalue approach has the ability to predict a more accurate stall point compare to RANS with a coarse computational grid. The investigation of the detailed flow field indicates that the flow structures in the vicinity of blade tip region change significantly with three different grid densities, the eigenvalue is also influenced. Two important flow mechanisms are found to be the decisive factors for the eigenvalue, namely the blockage generated by the shock-vortex interaction, the separated flow and the wake near the trailing edge. These flow patterns are consistent with the flow mechanisms of the compressor stall inception. Further investigations are conducted with four different turbulence models combined with three different spatial discretization schemes. Calculated eigenvalue proves that the turbulence model changes the eigenvalue with an over-prediction of stall point at about 1%. The spatial discretization scheme has small effect on stall point prediction using k-ε and SA models, whereas it has large effect when using SST model. The scheme shows great influence in the simulations with specific turbulence model by changing the predicted stall point at least 1.7%. The existence of blockage, the separation and the wake flow are identified as the major and secondary factor which contributes to an unstable prediction of eigenvalue approach, respectively.
APA, Harvard, Vancouver, ISO, and other styles
7

Lungenstrass, T., and G. D. Raikov. "Trace formulae for the asymptotic density of eigenvalue clusters for the perturbed Landau Hamiltonian." In QMath12 – Mathematical Results in Quantum Mechanics. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814618144_0002.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Tammen, Marvin, Ina Kodrasi, and Simon Doclo. "Complexity Reduction of Eigenvalue Decomposition-Based Diffuse Power Spectral Density Estimators Using the Power Method." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8462450.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Lohmayer, R., Herbert Neuberger, and Tilo Wettig. "Infinite-N limit of the eigenvalue density of Wilson loops in 2D SU(N) YM." In The XXVII International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2010. http://dx.doi.org/10.22323/1.091.0220.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Chung, Moon-Sun, Youn-Gyu Jung, and Sung-Jae Yi. "Numerical Calculation of Two-Phase Flow Based on a Two-Fluid Model With Flow Regime Transitions." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82781.

Full text
Abstract:
Numerical test and eigenvalue analysis for a two-phase channel flows for energy conversion systems like fuel cells or water electrolysers with flow regime transitions are performed by using the well-posed system of equation that takes into account the pressure jump at the phasic interface. The interfacial pressure jump terms derived from the definition of surface tension which is based on the surface physics make the conventional two-fluid model hyperbolic without any additive terms, i.e., virtual mass or artificial viscosity terms. The four-equation system has three sets of eigenvalues; each of them has an analytical form of real eigenvalues relevant to the sonic speeds with phasic velocities of three typical flow regimes such as dispersed, slug, and separated flows. Further, the eigenvalues for the flow transition regions can also be obtained numerically for smooth calculation of flow regime transitions. The sonic speeds agree well not only with the earlier experimental data but also with those of an analytical model. Owing to the hyperbolicity of this model, we can adopt an upwind method, which is one of the well-known Godunov type upwind methods. A typical example of two-phase flows shows that the present model can simulate the phase separation caused by density difference of two-phase fluids.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Density eigenvalue' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography