Quenched Exit Times for Random Walk on Dynamical Percolation

#### Y. Peres, P. Sousi, J.E. Steif

2018, v.24, Issue 5, 715-732

ABSTRACT

We consider random walk on dynamical percolation on the discrete torus $\Z_n^d$. In previous work, mixing times of this process for $p<p_c(\Z^d)$ were obtained in the annealed
setting where one averages over the dynamical percolation environment. Here
we study exit times in the {\em quenched} setting, where we condition on a typical dynamical percolation environment. We obtain an upper bound for all $p$ which for $p<p_c$ matches the known upper bound.

Keywords: dynamical percolation, random walk, hitting times, mixing times