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- Title
Gibbs/Metropolis algorithms on a convex polytope.
- Authors
Diaconis, Persi; Lebeau, Gilles; Michel, Laurent
- Abstract
This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyl-type inequalities. The top eigenvalues of the Markov chain are closely related to the Neumann eigenvalues of the polytope for a novel Laplacian.
- Subjects
ALGORITHMS; CONVEX polytopes; EIGENFUNCTIONS; EIGENVALUES; MARKOV processes
- Publication
Mathematische Zeitschrift, 2012, Vol 272, Issue 1/2, p109
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0924-5