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

MacPhee, Iain M. and Menshikov, Mikhail V. and Volkov, Stanislav and Wade, Andrew (2010) Passage-time moments and hybrid zones for the exclusion-voter model. Bernoulli, 16 (4). pp. 1312-1342.

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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.

Item type: Article
ID code: 29124
Keywords: almost-sure bounds, exclusion process , hybrid zone, voter model , passage-time moments , lyapunov functions , Probabilities. Mathematical statistics, Statistics and Probability
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 22 Mar 2011 12:21
Last modified: 24 Jul 2015 09:43
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/29124

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