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Long Term Behaviour of a Reversible System of Interacting Random Walks
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Royal Holloway Univ London, Egham, Surrey, England.
Lund Univ, Lund, Sweden.
2019 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 175, no 1, p. 71-96Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER , 2019. Vol. 175, no 1, p. 71-96
Keywords [en]
Markov chain, Random walk, Transience, Recurrence, Lyapunov function, Martingale, Renewal measure, Return time
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-381570DOI: 10.1007/s10955-019-02244-0ISI: 000462211500004OAI: oai:DiVA.org:uu-381570DiVA, id: diva2:1304534
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council, VR2014-5157Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved

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