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تسجيل مستخدم جديدSpectral asymptotics for Metropolis algorithm on singular domains
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تأليف
Laurent Michel
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We study the Metropolis algorithm on a bounded connected domain $Omega$ of the euclidean space with proposal kernel localized at a small scale $h > 0$. We consider the case of a domain $Omega$ 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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