Central Limit Theorem for a Random Walk with Random Obstacles in $\mathrm{R}^d$

Abstract

A random walk with obstacles in $\mathbf{R}^d, d \geq 2$, is considered. A probability measure is put on a space of obstacles, giving a random walk with random obstacles. A central limit theorem is then proven for this process when the obstacles are distributed by a Gibbs state with sufficiently low activity. The same problem is treated for a tagged particle of an infinite hard core particle system.