Front Propagation in an Exclusion One-dimensional Reactive Dynamics

M. Jara, G. Moreno, A.F. Ramirez

2008, v.14, Issue 2, 185-206

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 positions are interchanged 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 by 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.

Keywords: regeneration times,exclusion process,random walks in random environment