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We introduce the notion of a critical constant $c_{r t}$ for recurrence of random walks on $G$ -spaces. For a subgroup $H$ of a finitely generated group $G$ the critical constant is an asymptotic invariant of the quotient $G$ -space $G / H$ . We show that for any infinite $G$ -space $c_{r t} \geq 1 / 2$ . We say that $G / H$ is very small if $c_{r t} < 1$ . For a normal subgroup $H$ the quotient space $G / H$ is very small if and only if it is finite. However, we give examples of infinite very small $G$ -spaces. We show also that critical constants for recurrence can be used...

Cut times for random walks on the discrete Heisenberg group

Sébastien Blachère (2003)

Annales de l'I.H.P. Probabilités et statistiques

Displaying 21 – 26 of 26

Convolution Semigroups and Resolvent Families of Measures on Hypergroups.

Convolutional attractors of stationary sequences of random measures on compact groups

Convolutions of probability measures on semigroups.

Coverings, Laplacians, and heat kernels of directed graphs.

Critical constants for recurrence of random walks on G -spaces

Cut times for random walks on the discrete Heisenberg group

Currently displaying 21 – 26 of 26

Critical constants for recurrence of random walks on $G$ -spaces