15:45
Fluctuations of the front in a one dimensional growth model
Abstract
We report on two joint works with Jeremy Quastel and Alejandro Ramirez, on an
interacting particle system which can be viewed as a combustion mechanism or a
chemical reaction.
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.