摘要：In Dynamical Percolation each edge is open with probability p, refreshing its status at rate \mu>0. This process was introduced in the 1990s by Haggstrom, Steif and the speaker, motivated by a question of Malliavin. Remarkable results on exceptional times in two dimensions were obtained by Schramm, Steif, Garban and Pete.

We study random walk on dynamical percolation in the lattice Z^d, where the walk moves along open edges at rate 1. Let p_c=p_c(d) denote the critical value for static percolation. In the critical regime p=p_c, we prove that if d=2 or d>10, then the mean squared displacement is O(t\mu^a) where a=a(d)>0. For p>p_c, we prove that the mean squared displacement is of order t, uniformly in 0<\mu<1, refining earlier results obtained with Sousi and Steif.  (For p<p_c and \mu<1, it is known that the mean squared displacement is of order t \mu.) We will show simulations to illustrate the process. (Joint work with Chenlin Gu, Jianping Jiang, Zhan Shi, Hao Wu and Fan Yang.)