Random walk on dynamical percolation

We study the behavior of random walk on dynamical percolation, which is a random walk that moves in an environment (graph) that changes over time. In this model, the edges of a graph G are either open or closed, and refresh their status at rate $\mu$. At the same time a random walker moves on G at rate 1 but only along edges which are open. The regime of interest here is when $\mu$ goes to zero as the number of vertices of G goes to infinity, since this creates long-range dependencies on the model. When G is the d-dimensional torus of side length n, we prove that in the subcritical regime, the mixing times is of order $n^2\mu$. We also obtain results concerning mean squared displacement and hitting times. This is a joint work with Yuval Peres and Jeff Steif.