The Annals of Probability

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

Hideki Tanemura

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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


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