 0770 Marek Biskup, Timothy M. Prescott
 Functional CLT for random walk among bounded random conductances
(194K, PDF)
Mar 24, 07

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. We consider the nearestneighbor simple random walk on $\Z^d$, $d\ge2$, driven by a field of i.i.d. random nearestneighbor conductances $\omega_{xy}\in[0,1]$. Apart from the requirement that the bonds with positive conductances percolate, we pose no restriction on the law of the $\omega$'s. We prove that, for a.e. realization of the environment, the path distribution of the walk converges weakly to that of nondegenerate, isotropic Brownian motion. The quenched functional CLT holds despite the fact that the local CLT may fail in $d\ge5$ due to anomalously slow decay of the probability that the walk returns to the starting point at a given time.
 Files:
0770.src(
0770.keywords ,
condRWsubmit.pdf.mm )