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Pré-Publication, Document De Travail Année : 2006

Fluctuations of the front in a one dimensional model of X+Y-->2X

Résumé

We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent continuous time, simple symmetric random walks. $Y$ particles are transformed instantaneously to $X$ particles upon contact. We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the right of the origin, and define a class of configurations of the $X$ particles to the left of the origin having a finite $l^1$ norm with a specified exponential weight. Starting from any configuration of $X$ particles to the left of the origin within such a class, we prove a central limit theorem for the position of the rightmost visited site of the $X$ particles.

Dates et versions

hal-00108095 , version 1 (19-10-2006)

Identifiants

Citer

Francis Comets, Jeremy Quastel, Alejandro F. Ramirez. Fluctuations of the front in a one dimensional model of X+Y-->2X. 2006. ⟨hal-00108095⟩
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