Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times

We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph are either open or closed and refresh their status at rate while at the same time a random walker moves on at rate 1 but only along edges which are open. On the -dimensional torus with side length , we prove that in the subcritical regime, the mixing times for both the full system and the random walker are up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the lattice holds for this model as well.