SPECTRAL ASYMPTOTICS FOR METROPOLIS ALGORITHM ON SINGULAR DOMAINS
Résumé
We study the Metropolis algorithm on a bounded connected domain Ω of the euclidean space with proposal kernel localized at a small scale h > 0. We consider the case of a domain Ω that may have cusp singularities. For small values of the parameter h we prove the existence of a spectral gap g(h) and study the behavior of g(h) when h goes to zero. As a consequence, we obtain exponentially fast return to equilibrium in total variation distance.
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