Abstract

We consider a model of the reaction X + Y ? 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 ? 1 of Y particles at each site to the right of the origin. We prove a central limit theorem for the rightmost visited site of the X particles up to time t and show that the law of the environment as seen from the front converges to a unique invariant measure. © 2009 American Mathematical Society.