## The Annals of Probability

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

Hideki Tanemura

#### 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.

#### Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 936-960.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989276

Digital Object Identifier
doi:10.1214/aop/1176989276

Mathematical Reviews number (MathSciNet)
MR1217574

Zentralblatt MATH identifier
0783.60108

JSTOR
Tanemura, Hideki. Central Limit Theorem for a Random Walk with Random Obstacles in $\mathrm{R}^d$. Ann. Probab. 21 (1993), no. 2, 936--960. doi:10.1214/aop/1176989276. https://projecteuclid.org/euclid.aop/1176989276