Abstract
It is shown that a locally compact metrizable group $G$ is compact if and only if every random walk on $G$ is recurrent.
Citation
A. Brunel. D. Revuz. "Un Critere Probabiliste de Compacite Des Groupes." Ann. Probab. 2 (4) 745 - 746, August, 1974. https://doi.org/10.1214/aop/1176996618
Information