Work

Full Γ-expansion of reversible Markov chains level two large deviations rate functionals

Year: 2024

Type: article

Abstract: Let Ξn⊂Rd, n≥1, be a sequence of finite sets and consider a Ξn-valued, irreducible, reversible, continuous-time Markov chain (Xt(n):t≥0). Denote by P(Rd) the set of probability measures on Rd and by In:P(Rd)→[0,+∞) the level two large deviations rate functional for Xt(n) as t→∞. We present a general method, based on tools used to prove the metastable behaviour of Markov chains, to derive a full expansion of In expressing it as In=I(0)+∑ 1≤p≤q(1/θn(p))I(p), where I(p):P(Rd)→[0,+∞] represent rate functionals independent of n and θn(p) sequences such that θn(1)→∞, θn(p)/θn(p+1)→0 for 1≤p

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2100

Authors: Claudio Landim, Ricardo Misturini, Federico Sau

Institutions: Centre National de la Recherche Scientifique, Laboratoire de Mathématiques Raphaël Salem, Universidade Federal do Rio Grande do Sul, University of Trieste

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro