SPECTRAL ASYMPTOTICS FOR METROPOLIS ALGORITHM ON SINGULAR DOMAINS

Laurent Michel (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Laurent Michel. SPECTRAL ASYMPTOTICS FOR METROPOLIS ALGORITHM ON SINGULAR DOMAINS. 2021. ⟨hal-03199521⟩