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.
Publié le : 1993-04-14
Classification:
Random walk with random obstacles,
tagged particle,
invariance principle,
Gibbs states,
percolation models,
60K35
@article{1176989276,
author = {Tanemura, Hideki},
title = {Central Limit Theorem for a Random Walk with Random Obstacles in $\mathrm{R}^d$},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 936-960},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989276}
}
Tanemura, Hideki. Central Limit Theorem for a Random Walk with Random Obstacles in $\mathrm{R}^d$. Ann. Probab., Tome 21 (1993) no. 4, pp. 936-960. http://gdmltest.u-ga.fr/item/1176989276/