We prove that, with probability 1, eventually there are no more than three favorite (i.e., most visited) sites of simple symmetric random walks. This partially answers a relatively longstanding question of Erdös and Révész.
"No more than three favorite sites for simple random walk." Ann. Probab. 29 (1) 484 - 503, February 2001. https://doi.org/10.1214/aop/1008956341