Skip to main content

Research Repository

Advanced Search

Passage-time moments and hybrid zones for the exclusion-voter model

MacPhee, Iain M.; Menshikov, Mikhail V.; Volkov, Stanislav; Wade, Andrew R.

Passage-time moments and hybrid zones for the exclusion-voter model Thumbnail


Authors

Iain M. MacPhee

Mikhail V. Menshikov

Stanislav Volkov



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.

Citation

MacPhee, I. M., Menshikov, M. V., Volkov, S., & Wade, A. R. (2010). Passage-time moments and hybrid zones for the exclusion-voter model. Bernoulli (Andover), 16(4), 1312-1342. https://doi.org/10.3150/09-bej243

Journal Article Type Article
Publication Date Nov 1, 2010
Deposit Date Feb 28, 2011
Publicly Available Date Jan 31, 2013
Journal Bernoulli - Journal of the Bernoulli Society
Print ISSN 1350-7265
Publisher Bernoulli Society for Mathematical Statistics and Probability
Peer Reviewed Peer Reviewed
Volume 16
Issue 4
Pages 1312-1342
DOI https://doi.org/10.3150/09-bej243
Keywords Almost-sure bounds, Exclusion process, Hybrid zone, Lyapunov functions, Passage-time moments, Voter model.

Files





You might also like



Downloadable Citations