2007/03/06 by Milton Jara, Gregorio Moreno, Jara, Milton +4
Mathematics · Physics and Astronomy · #60F17 #82C22 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F17 #msc:82C22
paper · pdf · doi:10.48550/arxiv.math/0703173
19 pages
arxiv created 2007/03/06 · openalex publication_date 2007/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ρ,0<ρ<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.