Favorite sites for simple random walk in two and more dimensions

We consider favorite sites, i.e., sites that achieve the maximal local time for a discrete time simple random walk. We show that the limsup of the number of favorite sites is 3 with probability one in d=2. We also give sharp asymptotics of the number in higher dimensions.

This talk is based on a joint work with Chenxu Hao (Peking), Xinyi Li (Peking) and Yushu Zheng (CAS).