Mathematics Colloquia and Seminars

We consider a simple random walk on the (unique) infinite cluster $C_\infty$ of bond percolation in $\mathbb Z^d$, $d\ge2$. At each unit of time the walk picks one of its $2d$ neighbors at random and attempts to move to it, but the move is suppressed if the respective edge is not present in $C_\infty$. We will show that, in almost every realization of $C_\infty$, the path of this walk scales to d-dimensional Brownian motion under the "usual" scaling of space and time. The proof is based on analysis of the "corrector" which is an additive term that makes the position of the walk a marti