Long Term Behaviour of a Reversible System of Interacting Random Walks
Janson, Svante ; Shcherbakov, Vadim and Volkov, Stanislav LU
(2019)
In Journal of Statistical Physics
175(1).
p.71-96
- 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... (More)
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.
(Less)
- author
- Janson, Svante
; Shcherbakov, Vadim
and Volkov, Stanislav
LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Lyapunov function, Markov chain, Martingale, Random walk, Recurrence, Renewal measure, Return time, Transience
- in
- Journal of Statistical Physics
- volume
- 175
- issue
- 1
- pages
- 71 - 96
- publisher
- Springer
- external identifiers
-
- scopus:85061183245
- ISSN
- 0022-4715
- DOI
- 10.1007/s10955-019-02244-0
- language
- English
- LU publication?
- yes
- id
- 9ccb3200-9bdc-4a26-bc64-e1ec65a2a232
- date added to LUP
- 2019-02-22 12:50:28
- date last changed
- 2022-04-25 21:31:48
@article{9ccb3200-9bdc-4a26-bc64-e1ec65a2a232,
abstract = {{<p>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.</p>}},
author = {{Janson, Svante and Shcherbakov, Vadim and Volkov, Stanislav}},
issn = {{0022-4715}},
keywords = {{Lyapunov function; Markov chain; Martingale; Random walk; Recurrence; Renewal measure; Return time; Transience}},
language = {{eng}},
number = {{1}},
pages = {{71--96}},
publisher = {{Springer}},
series = {{Journal of Statistical Physics}},
title = {{Long Term Behaviour of a Reversible System of Interacting Random Walks}},
url = {{http://dx.doi.org/10.1007/s10955-019-02244-0}},
doi = {{10.1007/s10955-019-02244-0}},
volume = {{175}},
year = {{2019}},
}