Semi-classical analysis of a random walk on a manifold

DOI10.1214/09-AOP483zbMath1187.58033arXiv0802.0644OpenAlexW3098905378MaRDI QIDQ2268701

Laurent Michel, Gilles Lebeau

Publication date: 8 March 2010

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0644

zbMATH Keywords

eigenvaluesRiemannian manifoldspectral theoryMarkov chainsemi-classical analysisrandom walkMetropolis algorithm

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (16)

Rapid mixing of geodesic walks on manifolds with positive curvature ⋮ Approximations of the connection Laplacian spectra ⋮ Random walks and approximate integration on compact homogeneous spaces ⋮ A geometric heat-flow theory of Lagrangian coherent structures ⋮ Quantization of symplectic fibrations and canonical metrics ⋮ Harnack inequalities and Gaussian estimates for random walks on metric measure spaces ⋮ Geometric analysis for the Metropolis algorithm on Lipschitz domains ⋮ Gibbs/Metropolis algorithms on a convex polytope ⋮ Spectral aspects of the Berezin transform ⋮ Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling ⋮ Random walk on surfaces with hyperbolic cusps ⋮ The Markov chain Monte Carlo revolution ⋮ Micro-local analysis for the Metropolis algorithm ⋮ Spectral stability of metric-measure Laplacians ⋮ Randomized interior point methods for sampling and optimization ⋮ Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry

Cites Work

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• Dirichlet forms and symmetric Markov processes
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Nonparametic estimation of location and dispersion on Riemannian manifolds
• Sampling from a Manifold
• An introduction to semiclassical and microlocal analysis

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