Graph-combinatorial approach for large deviations of Markov chains

Giorgio Carugno; Pierpaolo Vivo; Francesco Coghi

doi:10.1088/1751-8121/ac79e6

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arXiv · 2201.00582

Graph-combinatorial approach for large deviations of Markov chains

Giorgio Carugno·Pierpaolo Vivo·Francesco Coghi

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Abstract

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.

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Giorgio Carugno, Pierpaolo Vivo, Francesco Coghi. 2022-01-03. Graph-combinatorial approach for large deviations of Markov chains. https://doi.org/10.1088/1751-8121%2Fac79e6

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