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.
Publié le : 1994-07-14
Classification:
Random walk,
concentration function,
adapted measure,
strictly aperiodic measure,
60B15,
60J15,
47A35
@article{1176988614,
author = {Bartoszek, Wojciech},
title = {On Concentration Functions on Discrete Groups},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1596-1599},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988614}
}
Bartoszek, Wojciech. On Concentration Functions on Discrete Groups. Ann. Probab., Tome 22 (1994) no. 4, pp. 1596-1599. http://gdmltest.u-ga.fr/item/1176988614/