Modul:   MAT971  Seminar über stochastische Prozesse

Quenched invariance principle for simple random walk on clusters of correlated percolation models

Vortrag von Dr. Ron Rosenthal

Datum: 16.10.13  Zeit: 17.15 - 18.15  Raum: ETH

We derive a quenched invariance principle for simple random walk on the unique infinite cluster for a general class of percolation models on $\mathbb{Z}^d$, $d\geq2$. This includes models with long-range correlations such as random interlacements in dimension $d\geq3$ at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness. An essential ingredient of our proof is a new isoperimetric inequality for this type of correlated percolation models. This is a joint work with Eviatar Procaccia and Artëm Sapozhnikov.