Passage-time moments and hybrid zones for the exclusion-voter model
MacPhee, Iain ; Menshikov, Mikhail ; Volkov, Stanislav LU
and Wade, Andrew
(2010)
In Bernoulli
16(4).
p.1312-1342
- Abstract
- We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from a finite perturbation of the ground state Heaviside configuration consisting of 1’s to the left of the origin and 0’s elsewhere, we study the relaxation time τ, that is, the first hitting time of the ground state configuration (up to translation). We give conditions for τ to be finite and for certain moments of τ to be finite or infinite, and prove a result that approaches a conjecture of Belitsky et al. (Bernoulli 7 (2001) 119–144). Ours are the first non-existence-of-moments results for τ for the mixture model. Moreover, we give almost sure asymptotics for the... (More)
- We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from a finite perturbation of the ground state Heaviside configuration consisting of 1’s to the left of the origin and 0’s elsewhere, we study the relaxation time τ, that is, the first hitting time of the ground state configuration (up to translation). We give conditions for τ to be finite and for certain moments of τ to be finite or infinite, and prove a result that approaches a conjecture of Belitsky et al. (Bernoulli 7 (2001) 119–144). Ours are the first non-existence-of-moments results for τ for the mixture model. Moreover, we give almost sure asymptotics for the evolution of the size of the hybrid (disordered) region. Most of our results pertain to the discrete-time setting, but several transfer to continuous-time. As well as the mixture process, some of our results also cover pure exclusion. We state several significant open problems. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4359856
- author
- MacPhee, Iain
; Menshikov, Mikhail
; Volkov, Stanislav
LU
and Wade, Andrew
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- almost-sure bounds, exclusion process, hybrid zone, Lyapunov functions, passage-time moments, voter model
- in
- Bernoulli
- volume
- 16
- issue
- 4
- pages
- 1312 - 1342
- publisher
- Chapman and Hall
- external identifiers
-
- scopus:79251547040
- ISSN
- 1350-7265
- DOI
- 10.3150/09-BEJ243
- language
- English
- LU publication?
- no
- id
- b6693c0f-1368-4602-a917-ab04df7cc0d9 (old id 4359856)
- alternative location
- http://projecteuclid.org/euclid.bj/1290092908
- date added to LUP
- 2016-04-01 10:11:54
- date last changed
- 2022-01-25 20:48:14
@article{b6693c0f-1368-4602-a917-ab04df7cc0d9,
abstract = {{We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from a finite perturbation of the ground state Heaviside configuration consisting of 1’s to the left of the origin and 0’s elsewhere, we study the relaxation time τ, that is, the first hitting time of the ground state configuration (up to translation). We give conditions for τ to be finite and for certain moments of τ to be finite or infinite, and prove a result that approaches a conjecture of Belitsky et al. (Bernoulli 7 (2001) 119–144). Ours are the first non-existence-of-moments results for τ for the mixture model. Moreover, we give almost sure asymptotics for the evolution of the size of the hybrid (disordered) region. Most of our results pertain to the discrete-time setting, but several transfer to continuous-time. As well as the mixture process, some of our results also cover pure exclusion. We state several significant open problems.}},
author = {{MacPhee, Iain and Menshikov, Mikhail and Volkov, Stanislav and Wade, Andrew}},
issn = {{1350-7265}},
keywords = {{almost-sure bounds; exclusion process; hybrid zone; Lyapunov functions; passage-time moments; voter model}},
language = {{eng}},
number = {{4}},
pages = {{1312--1342}},
publisher = {{Chapman and Hall}},
series = {{Bernoulli}},
title = {{Passage-time moments and hybrid zones for the exclusion-voter model}},
url = {{http://dx.doi.org/10.3150/09-BEJ243}},
doi = {{10.3150/09-BEJ243}},
volume = {{16}},
year = {{2010}},
}