（本セミナーは確率論セミナーとの合同開催です．） In Dynamical Percolation each edge is open with probability p, refreshing its status at rate r>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 d dimensional lattice, 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 r^a) where a=a(d)>0. For p>p_c, we prove that the mean squared displacement is of order t, uniformly in 0<r<1, refining earlier results obtained by the speaker with Sousi and Steif. We will show simulations to illustrate the process. (Joint work with Chenlin Gu, Jianping Jiang, Zhan Shi, Hao Wu and Fan Yang.)