## The Annals of Probability

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

### 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Random walk with random obstacles tagged particle invariance principle Gibbs states percolation models

#### Citation

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