Speaker
Description
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 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 $O(t r^a)$ where $a=a(d)>0$. For $p>p_c$, we prove that the mean squared displacement is of order $t$, uniformly in $0 (If $p Joint work with Chenlin Gu, Jianping Jiang, Zhan Shi, Hao Wu and Fan Yang.
