Law of the Iterated Logarithm for the random walk on the infinite percolation cluster

Details Law of the Iterated Logarithm for the random walk on the infinite percolation cluster Law of the Iterated Logarithm for the random walk on the infinite percolation cluster

2008-09-25

arxiv.org/abs/0809.4380v1

Mathematics

Probability

10 pages

Scientific paper

We show that random walks on the infinite supercritical percolation clusters
in Z^d satisfy the usual Law of the Iterated Logarithm. The proof combines
Barlow's Gaussian heat kernel estimates and the ergodicity of the random walk
on the environment viewed from the random walker as derived by Berger and
Biskup.

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