Long Term Behaviour of a Reversible System of Interacting Random Walks. / Janson, Svante; Shcherbakov, Vadim; Volkov, Stanislav.

In: Journal of Statistical Physics, Vol. 175, No. 1, 04.2019, p. 71-96.

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Long Term Behaviour of a Reversible System of Interacting Random Walks. / Janson, Svante; Shcherbakov, Vadim; Volkov, Stanislav.

In: Journal of Statistical Physics, Vol. 175, No. 1, 04.2019, p. 71-96.

Research output: Contribution to journalArticle

Harvard

Janson, S, Shcherbakov, V & Volkov, S 2019, 'Long Term Behaviour of a Reversible System of Interacting Random Walks', Journal of Statistical Physics, vol. 175, no. 1, pp. 71-96. https://doi.org/10.1007/s10955-019-02244-0

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Author

Janson, Svante ; Shcherbakov, Vadim ; Volkov, Stanislav. / Long Term Behaviour of a Reversible System of Interacting Random Walks. In: Journal of Statistical Physics. 2019 ; Vol. 175, No. 1. pp. 71-96.

BibTeX

@article{087dcb2ef2314ab48b9d0ca249593b7b,
title = "Long Term Behaviour of a Reversible System of Interacting Random Walks",
abstract = "This paper studies the long-term behaviour of a system of interacting random walks labelled by vertices of a finite graph. We show that the system undergoes phase transitions, with different behaviour in various regions, depending on model parameters and properties of the underlying graph. We provide the complete classification of the long-term behaviour of the corresponding continuous time Markov chain, identifying whether it is null recurrent, positive recurrent, or transient. The proofs are partially based on the reversibility of the model, which allows us to use the method of electric networks. We also provide some alternative proofs (based on the Lyapunov function method and the renewal theory), which are of interest in their own right, since they do not require reversibility and can be applied to more general situations.",
author = "Svante Janson and Vadim Shcherbakov and Stanislav Volkov",
year = "2019",
month = apr,
doi = "10.1007/s10955-019-02244-0",
language = "English",
volume = "175",
pages = "71--96",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "1",

}

RIS

TY - JOUR

T1 - Long Term Behaviour of a Reversible System of Interacting Random Walks

AU - Janson, Svante

AU - Shcherbakov, Vadim

AU - Volkov, Stanislav

PY - 2019/4

Y1 - 2019/4

N2 - This paper studies the long-term behaviour of a system of interacting random walks labelled by vertices of a finite graph. We show that the system undergoes phase transitions, with different behaviour in various regions, depending on model parameters and properties of the underlying graph. We provide the complete classification of the long-term behaviour of the corresponding continuous time Markov chain, identifying whether it is null recurrent, positive recurrent, or transient. The proofs are partially based on the reversibility of the model, which allows us to use the method of electric networks. We also provide some alternative proofs (based on the Lyapunov function method and the renewal theory), which are of interest in their own right, since they do not require reversibility and can be applied to more general situations.

AB - This paper studies the long-term behaviour of a system of interacting random walks labelled by vertices of a finite graph. We show that the system undergoes phase transitions, with different behaviour in various regions, depending on model parameters and properties of the underlying graph. We provide the complete classification of the long-term behaviour of the corresponding continuous time Markov chain, identifying whether it is null recurrent, positive recurrent, or transient. The proofs are partially based on the reversibility of the model, which allows us to use the method of electric networks. We also provide some alternative proofs (based on the Lyapunov function method and the renewal theory), which are of interest in their own right, since they do not require reversibility and can be applied to more general situations.

U2 - 10.1007/s10955-019-02244-0

DO - 10.1007/s10955-019-02244-0

M3 - Article

VL - 175

SP - 71

EP - 96

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -