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We study the behavior of random walk on dynamical percolation. In this model,the edges of a graph G are either open or closed and refresh their status atrate \mu\ while at the same time a random walker moves on G at rate 1 but onlyalong edges which are open. On the d-dimensional torus with side length n, weprove that in the subcritical regime, the mixing times for both the full systemand the random walker are n^2/\mu\ up to constants. We also obtain resultsconcerning mean squared displacement and hitting times. Finally, we show thatthe usual recurrence transience dichotomy for the lattice Z^d holds for thismodel as well.

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