Quenched exit times for random walk on dynamical percolation

We consider random walk on dynamical percolation on the discrete torus ${\mathbb{Z}}_n^d$. In previous work, mixing times of this process for $p<p_c({\mathbb{Z}}^d)$ were obtained in the annealed setting where one averages over the dynamical percolation environment. Here we study exit times in the 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 lower bound.