Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times
Artikel i vetenskaplig tidskrift, 2015
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 at rate mu while at the same time a random walker moves
on G at rate 1 but only along edges which are open. On the d-dimensional torus with side length n, we
prove that in the subcritical regime, the mixing times for both the full system and the random walker are
n^2/mu 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 Z^d holds for this model as well.