Abstract
Let $(\xi_n)_{n \geq 0}$ be a random walk on a countable group $G$. Sufficient and necessary conditions for the existence of a finite set $A \subseteq G$ and a sequence $g_n \in G$ such that for all natural $n$ we have $P(\xi_n \in A\mid\xi_0 = g_n) = 1$ are presented. This provides a complete solution to the problem of behavior of concentration functions on discrete groups.
Citation
Wojciech Bartoszek. "On Concentration Functions on Discrete Groups." Ann. Probab. 22 (3) 1596 - 1599, July, 1994. https://doi.org/10.1214/aop/1176988614
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