2016
DOI: 10.1016/j.spa.2015.11.015
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Metastable states, quasi-stationary distributions and soft measures

Abstract: ABSTRACT. 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 ensemble and quasi-stationary measures, and introducing soft measures as interpolation between the two, we prove asymptotic exponential exit law and, on a generally different time scale, asymptotic exponential transition law. By using potential-theoretic tools, and introducing "(κ, λ)-capacities", we … Show more

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Cited by 47 publications
(54 citation statements)
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“…• Other general Markov processes having metastable states; see, e.g., [57][58][59] and references therein. The occupation set S defining the conditioning can be chosen to include one or more metastable states or a set of states connecting stable and metastable states so as to study transition pathways, also called reactive paths.…”
Section: Discussionmentioning
confidence: 99%
“…• Other general Markov processes having metastable states; see, e.g., [57][58][59] and references therein. The occupation set S defining the conditioning can be chosen to include one or more metastable states or a set of states connecting stable and metastable states so as to study transition pathways, also called reactive paths.…”
Section: Discussionmentioning
confidence: 99%
“…Since its first rigorous mathematical treatment [20,16,10,23,9], metastability has been the subject of intensive investigation from different perspectives [13,1,22,6,14].…”
Section: Introductionmentioning
confidence: 99%
“…The quantity on the right hand side of (1.19) bears some similarity to the Cheeger constant [23] on weighted graphs [32] defined by In the paper [10], metastability has alternatively been characterized in terms of ratios ǫ between Dirichlet and Neumann spectral gaps of restricted generators. For this purpose the state space is decomposed into two sets = ∪ c .…”
Section: Main Resultmentioning
confidence: 99%