Relevant bibliographies by topics / Heat kernel asymptotics

Academic literature on the topic 'Heat kernel asymptotics'

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Published: 14 March 2023

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Journal articles on the topic "Heat kernel asymptotics"

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BÄR, CHRISTIAN, and SERGIU MOROIANU. "HEAT KERNEL ASYMPTOTICS FOR ROOTS OF GENERALIZED LAPLACIANS." International Journal of Mathematics 14, no. 04 (June 2003): 397–412. http://dx.doi.org/10.1142/s0129167x03001788.

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We describe the heat kernel asymptotics for roots of a Laplace type operator Δ on a closed manifold. A previously known relation between the Wodzicki residue of Δ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.
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Baudoin, Fabrice. "Stochastic Taylor expansions and heat kernel asymptotics." ESAIM: Probability and Statistics 16 (2012): 453–78. http://dx.doi.org/10.1051/ps/2011107.

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McAvity, D. M. "Heat kernel asymptotics for mixed boundary conditions." Classical and Quantum Gravity 9, no. 8 (August 1, 1992): 1983–97. http://dx.doi.org/10.1088/0264-9381/9/8/017.

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Bolte, Jens, and Stefan Keppeler. "Heat kernel asymptotics for magnetic Schrödinger operators." Journal of Mathematical Physics 54, no. 11 (November 2013): 112104. http://dx.doi.org/10.1063/1.4829061.

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Branson, Thomas P., Peter B. Gilkey, Klaus Kirsten, and Dmitri V. Vassilevich. "Heat kernel asymptotics with mixed boundary conditions." Nuclear Physics B 563, no. 3 (December 1999): 603–26. http://dx.doi.org/10.1016/s0550-3213(99)00590-8.

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Kirsten, Klaus. "Heat kernel asymptotics: more special case calculations." Nuclear Physics B - Proceedings Supplements 104, no. 1-3 (January 2002): 119–26. http://dx.doi.org/10.1016/s0920-5632(01)01598-5.

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Revelle, David. "Heat Kernel Asymptotics on the Lamplighter Group." Electronic Communications in Probability 8 (2003): 142–54. http://dx.doi.org/10.1214/ecp.v8-1092.

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AVRAMIDI, IVAN G., and THOMAS BRANSON. "HEAT KERNEL ASYMPTOTICS OF OPERATORS WITH NON-LAPLACE PRINCIPAL PART." Reviews in Mathematical Physics 13, no. 07 (July 2001): 847–90. http://dx.doi.org/10.1142/s0129055x01000892.

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We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part -∇μ∇μ. Our objective is to obtain information on the asymptotic expansions of the corresponding resolvent and the heat kernel. The heat kernel and the Green's function are constructed explicitly in the leading order. The first two coefficients of the heat kernel asymptotic expansion are computed explicitly. A new semi-classical ansatz as well as the complete recursion system for the heat kernel of non-Laplace type operators is constructed. Some particular cases are studied in more detail.
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Avramidi, Ivan G. "Heat Kernel Asymptotics of Zaremba Boundary Value Problem." Mathematical Physics, Analysis and Geometry 7, no. 1 (2004): 9–46. http://dx.doi.org/10.1023/b:mpag.0000022837.63824.4c.

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Mooers, Edith A. "Heat kernel asymptotics on manifolds with conic singularities." Journal d'Analyse Mathématique 78, no. 1 (December 1999): 1–36. http://dx.doi.org/10.1007/bf02791127.

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Dissertations / Theses on the topic "Heat kernel asymptotics"

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Li, Liangpan. "Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/23004.

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In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method. In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle, we obtain certain asymptotic estimates about the integral kernel of heat operators. As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel. Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.
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Grieger, Elisabeth Sarah Francis. "On heat kernel methods and curvature asymptotics for certain cohomogeneity one Riemannian manifolds." Thesis, King's College London (University of London), 2016. http://kclpure.kcl.ac.uk/portal/en/theses/on-heat-kernel-methods-and-curvature-asymptotics-for-certain-cohomogeneity-one-riemannian-manifolds(40d2e3ab-3eb8-4141-bcc5-ca38e0705f65).html.

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We study problems related to the metric of a Riemannian manifold with a particular focus on certain cohomogeneity one metrics. In Chapter 2 we study a set of cohomogeneity one Einstein metrics found by A. Dancer and M. Wang. We express these in terms of elementary functions and nd explicit sectional curvature formulae which are then used to determine sectional curvature asymptotics of the metrics. In Chapter 3 we construct a non-standard parametrix for the heat kernel on a product manifold with multiply warped Riemannian metric. The special feature of this parametrix is that it separates the contribution of the warping functions and the heat data on the factors; this cannot be achieved via the standard approach. In Chapter 4 we determine explicit formulae for the resolvent symbols associated with the Laplace Beltrami operator over a closed Riemannian manifold and apply these to motivate an alternative method for computing heat trace coecients. This method is entirely based on local computations and to illustrate this we recover geometric formulae for the heat coecients. Furthermore one can derive topological identities via this approach; to demonstrate this application we nd explicit formulae for the resolvent symbols associated with Laplace operators on a Riemann surface and recover the Riemann-Roch formula. In the nal chapter we report on an area of current research: we introduce a class of symbols for pseudodi erential operators on simple warped products which is closed under composition. We then extend the canonical trace to this setting, using a cut - o integral, and nd an explicit formula for the extension in terms of integrals over the factor.
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Oikonomopoulos, Dimitrios [Verfasser]. "Functional Inequalities and Heat Kernel Asymptotics on Some Classes of Singular Riemannian Manifolds / Dimitrios Oikonomopoulos." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1200019814/34.

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Nakamura, Chikara. "Asymptotic behaviors of random walks; application of heat kernel estimates." Kyoto University, 2018. http://hdl.handle.net/2433/232222.

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Marsili, Paolo. "Short time asymptotic behaviors of Heat kernel and Brownian motion on a Riemannian manifold." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13541/.

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Xu, Chuan-yi. "On the asymptotic expansion of the trace of the the [sic] heat kernel for a subelliptic operator." Thesis, Massachusetts Institute of Technology, 1987. https://hdl.handle.net/1721.1/129500.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
Includes bibliographical references (leaves 89-91).
Chuan-yi Xu.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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SEGUIN, CAROLINE. "Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups." Thesis, 2011. http://hdl.handle.net/1974/6834.

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This thesis suggests an approach to compute the short-time behaviour of the hypoelliptic heat kernel corresponding to sub-Riemannian structures on unimodular Lie groups of type I, without previously holding a closed form expression for this heat kernel. Our work relies on the use of classical non-commutative harmonic analysis tools, namely the Generalized Fourier Transform and its inverse, combined with the Trotter product formula from the theory of perturbation of semigroups. We illustrate our main results by computing, to our knowledge, a first expression in short-time for the hypoelliptic heat kernel on the Engel and the Cartan groups, for which there exist no closed form expression.
Thesis (Master, Mathematics & Statistics) -- Queen's University, 2011-10-08 01:32:32.896
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Hu, Nai-Yo, and 胡乃友. "Heat kernel asymptotic expansions for Schrödinger operator on R^n." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/24tbf3.

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碩士
國立臺灣大學
數學研究所
105
In this thesis, we study the expression of the heat kernel of the Schrodinger operator in Euclidean space and its asymptotic expansion. We start by observing the behavior of the constant coefficient Schr"odinger operator in Euclidean space and introduce the new symbol space, and write down the expression of the heat kernel by the approximation method. It''s proved the existence and uniqueness of the heat kernel for the Schr"odinger operator in Euclidean space, and the asymptotic expansion of the heat kernel at time is approach to 0.
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Ruan, Jia-Xian, and 阮家賢. "Asymptotics to Heat Kernels of subLaplace Operators on the Heisenberg Group." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/91108206235694677424.

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碩士
輔仁大學
數學系碩士班
102
An integral form of the heat kernel for the subLaplace operator on Heisenberg groups was well known. In this thesis, we apply the complex integral, Laplace method, and the steepest descent method to calculate the asymptotic expansions of the heat kernel.
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Books on the topic "Heat kernel asymptotics"

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Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
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Book chapters on the topic "Heat kernel asymptotics"

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Avramidi, Ivan G. "Heat Kernel Asymptotics." In Heat Kernel Method and its Applications, 197–238. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-26266-6_5.

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Holcman, David, and Zeev Schuss. "Short-Time Asymptotics of the Heat Kernel." In Applied Mathematical Sciences, 159–87. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76895-3_5.

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Franchi, Jacques. "Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel." In Lecture Notes in Mathematics, 71–103. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11970-0_4.

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Duan, Xiaoxi. "The Heat Kernel and Green Function of the Sub-Laplacian on the Heisenberg Group." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 55–75. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_3.

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Molahajloo, Shahla, and M. W. Wong. "The Heat Kernel and Green Function of a Sub-Laplacian on the Hierarchical Heisenberg Group." In Pseudo-Differential Operators, Generalized Functions and Asymptotics, 85–102. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_5.

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Watling, Keith D. "Formulæ for the heat kernel of an elliptic operator exhibiting small-time asymptotics." In Lecture Notes in Mathematics, 167–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0077926.

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Holcman, David, and Zeev Schuss. "Short-Time Asymptotics of the Heat Kernel and Extreme Statistics of the NET." In Applied Mathematical Sciences, 311–40. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76895-3_9.

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Hashimoto, Yasuji, Shojiro Manabe, and Yukio Ogura. "Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion." In Itô’s Stochastic Calculus and Probability Theory, 129–39. Tokyo: Springer Japan, 1996. http://dx.doi.org/10.1007/978-4-431-68532-6_8.

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Berline, Nicole, Ezra Getzler, and Michèle Vergne. "Asymptotic Expansion of the Heat Kernel." In Heat Kernels and Dirac Operators, 61–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-58088-8_3.

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Kunita, Hiroshi. "Short Time Asymptotics of Random Heat Kernels." In Control of Distributed Parameter and Stochastic Systems, 231–38. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-0-387-35359-3_28.

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Conference papers on the topic "Heat kernel asymptotics"

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Stepin, S. A., Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Feynman-Kac formula: regularized trace and short-time asymptotics of the heat kernel." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043856.

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HARRISON, J. M., and K. KIRSTEN. "VACUUM ENERGY, SPECTRAL DETERMINANT AND HEAT KERNEL ASYMPTOTICS OF GRAPH LAPLACIANS WITH GENERAL VERTEX MATCHING CONDITIONS." In Proceedings of the Ninth Conference. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814289931_0052.

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Osipov, Alexander A. "Generalized Heat Kernel Coefficients for a New Asymptotic Expansion." In HADRON PHYSICS: Effective Theories of Low Energy QCD Second International Workshop on Hadron Physics. AIP, 2003. http://dx.doi.org/10.1063/1.1570560.

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Joyot, Pierre, Nicolas Verdon, Gaël Bonithon, Francisco Chinesta, and Pierre Villon. "PGD-BEM Applied to the Nonlinear Heat Equation." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82407.

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The Boundary Element Method (BEM) allows efficient solution of partial differential equations whose kernel functions are known. The heat equation is one of these candidates when the thermal parameters are assumed constant (linear model). When the model involves large physical domains and time simulation intervals the amount of information that must be stored increases significantly. This drawback can be circumvented by using advanced strategies, as for example the multi-poles technique. We propose radically different approach that leads to a separated solution of the space and time problems within a non-incremental integration strategy. The technique is based on the use of a space-time separated representation of the unknown field that, introduced in the residual weighting formulation, allows to define a separated solution of the resulting weak form. The spatial step can be then treated by invoking the standard BEM for solving the resulting steady state problem defined in the physical space. Then, the time problem that results in an ordinary first order differential equation is solved using any standard appropriate integration technique (e.g. backward finite differences). When considering the nonlinear heat equation, the BEM cannot be easily applied because its Green’s kernel is generally not known but the use of the PGD presents the advantage of rewriting the problem in such a way that the kernel is now clearly known. Indeed, the system obtained by the PGD is composed of a Poisson equation in space coupled with an ODE in time so that the use of the BEM for solving the spatial part of the problem is efficient. During the solving, we must however separate the nonlinear term into a space-time representation that can limit the method in terms of CPU time and storage, that is why we introduce in the second part of the paper a new approach combining the PGD and the Asymptotic Numerical Method (ANM) in order to efficiently treat the nonlinearity.
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YAJIMA, S., M. FUKUDA, S. TOKUO, S. I. KUBOTA, Y. HIGASHIDA, and Y. KAMO. "AN IRREDUCIBLE FORM FOR THE ASYMPTOTIC EXPANSION COEFFICIENTS OF THE HEAT KERNEL OF FERMIONS." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0485.

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