Graph-combinatorial approach for large deviations of Markov chains

被引：13

作者：

Carugno, Giorgio ^{[1
]}

Vivo, Pierpaolo ^{[1
]}

Coghi, Francesco ^{[2
,3
]}

机构：

[1] Kings Coll London, Dept Math, London WC2R 2LS, England

[2] KTH Royal Inst Technol, NORDITA, Hannes Alfvens vag 12, SE-10691 Stockholm, Sweden

[3] Stockholm Univ, Hannes Alfvens vag 12, SE-10691 Stockholm, Sweden

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2022年 / 55卷 / 29期

基金：

英国工程与自然科学研究理事会;

关键词：

large deviations; Markov chains; graph theory; jump-type observables; nonequilibrium free energy; SPECTRAL THEORY; LIMIT-THEOREMS; PROBABILITIES;

D O I：

10.1088/1751-8121/ac79e6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider discrete-time Markov chains and study large deviations of the pair empirical occupation measure, which is useful to compute fluctuations of pure-additive and jump-type observables. We provide an exact expression for the finite-time moment generating function, which is split in cycles and paths contributions, and scaled cumulant generating function of the pair empirical occupation measure via a graph-combinatorial approach. The expression obtained allows us to give a physical interpretation of interaction and entropic terms, and of the Lagrange multipliers, and may serve as a starting point for sub-leading asymptotics. We illustrate the use of the method for a simple two-state Markov chain.

引用

页数：24

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