Diffusions on graphs, Poisson problems and spectral geometry

DOI10.1090/S0002-9947-02-02973-2zbMath1015.58013arXivmath/0205097MaRDI QIDQ3151270

Robert Meyers, Patrick McDonald

Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0205097

zbMATH Keywords

heat equationvariational principlesStirling numbersrandom walkzeta functionsPoisson problemspectral graph theory

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Probabilistic potential theory (60J45) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (4)

Dirichlet spectrum and heat content ⋮ Graph characteristics from the heat kernel trace ⋮ Isospectral polygons, planar graphs and heat content ⋮ Kernel Density Estimation on a Linear Network

Cites Work

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• Geometric bounds for eigenvalues of Markov chains
• Brownian motion and random walks on manifolds
• Isoperimetric inequalities and Markov chains
• Random walks on graphs with a strong isoperimetric property
• Exit time moments, boundary value problems, and the geometry of domains in Euclidean space
• Heat content asymptotics of a Riemannian manifold with boundary
• Difference operators, covering spaces and determinants
• Determinants of Laplacians on graphs
• Discrete potential theory
• Variational principles for average exit time moments for diffusions in Euclidean space
• Algebraic Potential Theory on Graphs
• Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
• Isoperimetric conditions, Poisson problems, and diffusions in Riemannian manifolds

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