Graph-combinatorial approach for large deviations of Markov chains

Giorgio Carugno Carugno; Pierpaolo Vivo; Francesco Coghi

doi:10.1088/1751-8121/ac79e6

Graph-combinatorial approach for large deviations of Markov chains

Giorgio Carugno Carugno, Pierpaolo Vivo, Francesco Coghi^*

^*Corresponding author for this work

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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.

Original language	English
Article number	295001
Journal	Journal of Physics A
Volume	55
Issue number	29
DOIs	https://doi.org/10.1088/1751-8121/ac79e6
Publication status	Published - 4 Jul 2022

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Graph-combinatorial approach for_CARUGNO_Publishedonline4July2022_GOLD VoR CC BYFinal published version, 1.73 MBLicence: CC BY

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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.",

author = "Carugno, {Giorgio Carugno} and Pierpaolo Vivo and Francesco Coghi",

note = "Funding Information: GC and FC are thankful to Gianmichele Di Matteo for insightful discussions and to Mayank Shreshtha for having designed figure . FC is grateful to Hugo Touchette for pointing to interesting literature in the topic and for the hospitality in Stellenbosch (South Africa) during the writing stage of the manuscript. GC is supported by the EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES, EP/L015854/1). Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by IOP Publishing Ltd.",

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AU - Vivo, Pierpaolo

AU - Coghi, Francesco

N1 - Funding Information: GC and FC are thankful to Gianmichele Di Matteo for insightful discussions and to Mayank Shreshtha for having designed figure . FC is grateful to Hugo Touchette for pointing to interesting literature in the topic and for the hospitality in Stellenbosch (South Africa) during the writing stage of the manuscript. GC is supported by the EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES, EP/L015854/1). Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.

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N2 - 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.

AB - 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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Graph-combinatorial approach for large deviations of Markov chains

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