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