# 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.
Type de document :
Article dans une revue
Markov Processes and Related Fields, Polymath, 2008, 14 (2), pp.185-206
Domaine :

https://hal.archives-ouvertes.fr/hal-00362308
Contributeur : Milton Jara <>
Soumis le : mardi 17 février 2009 - 18:59:39
Dernière modification le : jeudi 11 janvier 2018 - 06:12:29

### Citation

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〉

### Métriques

Consultations de la notice