Metastability from the large deviations point of view: A Γ-expansion of the level two large deviations rate functional of non-reversible finite-state Markov chains

被引：0
作者：
Landim, C. [1 ,2 ]
机构：
[1] IMPA, Estr Dona Castorina 110, BR-22460 Rio De Janeiro, Brazil
[2] Univ Rouen, CNRS, UMR 6085, Ave Univ,BP12,Technopole Madrillet, F-76801 St Etienne Du Rouvray, France
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2023年 / 165卷
关键词：
Metastability; Large deviations; Continuous-time Markov processes on discrete state spaces; GLAUBER DYNAMICS; DIFFUSION-PROCESSES; KAWASAKI DYNAMICS; SHARP ASYMPTOTICS; DROPLETS; BEHAVIOR; MODEL; TIME;
D O I：
10.1016/j.spa.2023.09.001
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Consider a sequence of continuous-time Markov chains (X-t((n)) : t = 0) evolving on a fixed finite state space V. Let I-n be the level two large deviations rate functional for X-t((n)), t, as t -> infinity. Under a hypothesis on the jump rates, we prove that I-n can be written as I-n = I-(0) + Sigma(1 <= p <= q)(1/theta((p))(n))I-(p) for some rate functionals I-(p). The weights theta((p))(n) correspond to the time-scales at which the sequence of Markov chains X-t((n)) exhibit a metastable behavior, and the zero level sets of the rate functionals I-(p) identify the metastable states. (c) 2023 Elsevier B.V. All rights reserved.
引用
收藏
页码：275 / 315
页数：41
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