"Favourite sites, favourite values and jumping sizes for random walk and Brownian motion"

Endre Csáki, Pál Révész and Zhan Shi

Summary: We determine: (a) the joint almost sure asymptotic behaviour of the most visited site and the maximum local time of one-dimensional simple random walk or Brownian motion; (b) the maximal jumping size of the most visited site. These solve two open problems of Erdös and Révész.

Keywords: Local time, favourite site, random walk, Brownian motion.

AMS 1991 subject classification: 60J55; 60J15; 60J65.