Metastable states, quasi-stationary distributions and soft measures

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• 作者：Alessandra Bianchi^a ; ^{bianchi@math.unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Alexandre Gaudilliè ; re^b ; ^{alexandre.gaudilliere@math.cnrs.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：82C26 ; 60J27 ; 60J75 ; 60J45
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：126
• 期：6
• 页码：1622-1680
• 全文大小：510 K

文摘

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypotheses for Markov chains on a finite configuration space in some asymptotic regime. By comparing restricted ensembles and quasi-stationary measures, and introducing soft measures as an interpolation between the two, we prove an asymptotic exponential exit law and, on a generally different time scale, an asymptotic exponential transition law. By using potential-theoretic tools, and introducing “(κ,λ)$(\kappa ,\lambda )$-capacities”, we give sharp estimates on relaxation time, as well as mean exit time and transition time. We also establish local thermalization on shorter time scales.