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

C. Landim

Stochastic Processes and their Applications, 2023, vol. 165, issue C, 275-315

Abstract: Consider a sequence of continuous-time Markov chains (Xt(n):t≥0) evolving on a fixed finite state space V. Let In be the level two large deviations rate functional for Xt(n), as t→∞. Under a hypothesis on the jump rates, we prove that In can be written as In=I(0)+∑1≤p≤q(1/θn(p))I(p) for some rate functionals I(p). The weights θn(p) correspond to the time-scales at which the sequence of Markov chains Xt(n) exhibit a metastable behavior, and the zero level sets of the rate functionals I(p) identify the metastable states.

Keywords: Metastability; Large deviations; Continuous-time Markov processes on discrete state spaces (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.09.001

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