Let be the jointly continuous local times of a one-dimensional Brownian motion and let . Let be any point z such that , a most visited site of Brownian motion. We prove that if , then
with an analogous result for simple random walk. This proves a conjecture of Lifshits and Shi.
"The rate of escape of the most visited site of Brownian motion." Electron. J. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-EJP916