Front propagation in an exclusion one-dimensional reactive dynamics

Abstract : We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$ particles. When an $X$ particle jumps to a site with a $Y$ particle, their position is intechanged and the $Y$ particle becomes an $X$ one. Initially, there is an arbitrary configuration of $X$ particles at sites $..., -1,0$, and $Y$ particles only at sites $1,2,...$, with a product Bernoulli law of parameter $\rho,0<\rho<1$. We prove a law of large numbers and a central limit theorem for the front defined by the right-most visited site of the $X$ particles at time $t$. These results corroborate Monte-Carlo simulations performed in a similar context. We also prove that the law of the $X$ particles as seen from the front converges to a unique invariant measure. The proofs use regeneration times: we present a direct way to define them within this context.
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Markov Processes and Related Fields, Polymath, 2008, 14 (2), pp.185-206
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https://hal.archives-ouvertes.fr/hal-00362308
Contributeur : Milton Jara <>
Soumis le : mardi 17 février 2009 - 18:59:39
Dernière modification le : mercredi 12 octobre 2016 - 01:07:05

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Milton Jara, Gregorio Moreno, Alejandro F. Ramirez. Front propagation in an exclusion one-dimensional reactive dynamics. Markov Processes and Related Fields, Polymath, 2008, 14 (2), pp.185-206. <hal-00362308>

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