Metastable states, quasi-stationary distributions and soft measures

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Bianchi, Alessandra¹  Gaudilliere, Alexandre² 

[1] Univ Padua, Dipartimento Matemat, Via Trieste 63, I-35121 Padua, Italy

[2] Aix Marseille Univ, Cent Marseille, CNRS, I2M,UMR 7373, F-13453 Marseille, France

关键词: Metastability;    Restricted ensemble;    Quasi-stationary measure;    Soft measures;    Exponential law;    Spectral gap;    Mixing time;    Potential theory;   

DOI  :  10.1016/j.spa.2015.11.015

来源: Elsevier

【 摘 要 】

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 (k,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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free