FULL Γ- EXPANSION OF REVERSIBLE MARKOV CHAINS LEVEL TWO LARGE DEVIATIONS RATE FUNCTIONALS

• 成果类型: Article
• 署名作者: Landim, Claudio; Misturini, Ricardo; Sau, Federico
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal do Rio Grande do Sul; University of Trieste
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2100
• 发表日期: 2024
• 页码: 5578-5614
• 关键词: blume-capel model; metastability; field; time

摘要

Let E-n subset of R-d, n >= 1, be a sequence of finite sets and consider a E-n-valued, irreducible, reversible, continuous-time Markov chain (X-t((n)):t >= 0). Denote by P(R-d) the set of probability measures on R-d and by I-n:P(R-d)->[0,+infinity) the level two large deviations rate functional for X(t )((n))as t ->infinity. We present a general method, based on tools used to prove the metastable behaviour of Markov chains, to derive a full expansion of InIn expressing it as I-n=I-(0)+& sum;(1 <= p <= q)(1/theta((p))(n))I-(p), where I-(p):P(R-d)->[0,+infinity] represent rate functionals independent of n and theta((p))(n )sequences such that theta((1))n -> 0 theta((p))(n)/theta((p+1))(n)-> 0 for 1 <= p