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Auteur : Grafiati

Publié le 14 mars 2023

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1

Michiels, W. Stability and stabilization of time-delay systems : An Eigenvalue-based approach. Philadelphia : Society for Industrial and Applied Mathematics, 2007.

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2

L, Merkle C., et Lewis Research Center, dir. Time-derivative preconditioning for viscous flows. Brook Park, Ohio : Sverdrup Technology, Inc., Lewis Research Center Group, 1991.

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3

1975-, Sims Robert, et Ueltschi Daniel 1969-, dir. Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I : American Mathematical Society, 2011.

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4

Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation et Wunsch, Jared, editor of compilation, dir. Evolution equations : Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. Providence, Rhode Island : American Mathematical Society, 2013.

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5

Dzhamay, Anton, Christopher W. Curtis, Willy A. Hereman et B. Prinari. Nonlinear wave equations : Analytic and computational techniques : AMS Special Session, Nonlinear Waves and Integrable Systems : April 13-14, 2013, University of Colorado, Boulder, CO. Providence, Rhode Island : American Mathematical Society, 2015.

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6

Spectral analysis, differential equations, and mathematical physics : A festschrift in honor of Fritz Gesztesy's 60th birthday. Providence, Rhode Island : American Mathematical Society, 2013.

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7

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban et Harry Randolph Hughes. Probability on algebraic and geometric structures : International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Sous la direction de Mohammed Salah-Eldin 1946- et Mukherjea Arunava 1941-. Providence, Rhode Island : American Mathematical Society, 2016.

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8

Stability, Control, and Computation for Time-Delay Systems : An Eigenvalue-Based Approach, Second Edition. SIAM-Society for Industrial and Applied Mathematics, 2014.

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9

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

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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.

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10

Time-derivative preconditioning for viscous flows. Brook Park, Ohio : Sverdrup Technology, Inc., Lewis Research Center Group, 1991.

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11

Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.

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12

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

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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.

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13

Ferrari, Patrik L., et Herbert Spohn. Random matrices and Laplacian growth. Sous la direction de Gernot Akemann, Jinho Baik et Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.39.

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This article reviews the theory of random matrices with eigenvalues distributed in the complex plane and more general ‘beta ensembles’ (logarithmic gases in 2D). It first considers two ensembles of random matrices with complex eigenvalues: ensemble C of general complex matrices and ensemble N of normal matrices. In particular, it describes the Dyson gas picture for ensembles of matrices with general complex eigenvalues distributed on the plane. It then presents some general exact relations for correlation functions valid for any values of N and β before analysing the distribution and correlations of the eigenvalues in the large N limit. Using the technique of boundary value problems in two dimensions and elements of the potential theory, the article demonstrates that the finite-time blow-up (a cusp–like singularity) of the Laplacian growth with zero surface tension is a critical point of the normal and complex matrix models.

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14

Michiels, Wim, et Silviu-Iulian Niculescu. Stability and Stabilization of Time-Delay Systems (Advances in Design & Control) (Advances in Design and Control). Society for Industrial & Applied Mathematics,U.S., 2007.

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15

Schehr, Grégory, Alexander Altland, Yan V. Fyodorov, Neil O'Connell et Leticia F. Cugliandolo, dir. Stochastic Processes and Random Matrices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.001.0001.

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The field of stochastic processes and random matrix theory (RMT) has been a rapidly evolving subject during the past fifteen years where the continuous development and discovery of new tools, connections, and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar–Parisi–Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the past twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensemble of random matrices. These chapters not only cover this topic in detail but also present more recent developments that have emerged from these discoveries, for instance in the context of low-dimensional heat transport (on the physics side) or in the context of integrable probability (on the mathematical side).

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16

Philipp, Barbara Lee. Eigenstructure-based model reduction of linear control systems with applications. 1993.

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17

Majumdar, Satya N. Random growth models. Sous la direction de Gernot Akemann, Jinho Baik et Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.38.

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This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.

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18

Nonlinear Dirac Equation : Spectral Stability of Solitary Waves. American Mathematical Society, 2020.

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