Metastable states, quasi-stationary distributions and soft measures

Alessandra Bianchi and Alexandre Gaudillière

Stochastic Processes and their Applications, 2016, vol. 126, issue 6, 1622-1680

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 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)-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.

Keywords: Metastability; Restricted ensemble; Quasi-stationary measure; Soft measures; Exponential law; Spectral gap; Mixing time; Potential theory (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:6:p:1622-1680

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DOI: 10.1016/j.spa.2015.11.015

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