No more than three favourite sites for simple random walk

TL;DR

This paper proves that with probability one, a simple random walk will eventually have no more than three most visited sites, addressing a long-standing open question in the field.

Contribution

It establishes that the number of favourite sites of a simple random walk is almost surely at most three eventually, providing a significant partial answer to a longstanding problem.

Findings

Almost sure upper bound of three favourite sites

Addresses a long-standing open problem

Advances understanding of local times in random walks

Abstract

We prove that, with probability one, eventually there are no more than three favourite (i.e. most visited) sites of simple random walk. This partially answers a relatively long standing question of Pal Erdos and Pal Revesz.