Favorite Sites for Simple Random Walk in Two and More Dimensions
Favorite Sites for Simple Random Walk in Two and More Dimensions
On the trace of a discrete-time simple random walk on $\mathbb{Z}^d$ for $d\geq 2$, we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at a certain time. For $d=2$, we show that almost surely three favorite sites occur simultaneously infinitely often and eventually there …