Strong ratio limit theorems associated with random walks

2015/11/09 by Shur, M. G.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.02811

Abstract

Strong ratio limit theorems associated with a broad class of spread out random walks on unimodular groups were proved in the preceding paper, where these random walks were assumed to have the convergence parameter R=1. In the present paper, we study the case of an arbitrary R≥1 and clarify the role of the condition that the group is unimodular.

Related

• A non-symmetric Kesten criterion and ratio limit theorem for random walks on amenable groups
• Some old and basic facts about random walks on groups
• Ratio-limit boundaries for random walks on relatively hyperbolic groups
• Ratio limits and pressure function for group extensions of Gibbs Markov maps
• Random walks on wreath products of groups