Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups

2025/07/21 by Dussaule, Matthieu
#FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.15408

Abstract

Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of p_n(e,e), the probability that the random walk at time n is at the origin. We give the classification of all possible local limit theorems, up to bounded error, for finitely supported, symmetric, admissible probability measures on a relatively hyperbolic group with respect to virtually nilpotent subgroups.

Citations

• Exotic local limit theorems at the phase transition in free products
• Local limit theorems in relatively hyperbolic groups II : the non-spectrally degenerate case
• Local limit theorems in relatively hyperbolic groups I : rough estimates
• Stability phenomena for Martin boundaries of relatively hyperbolic groups
• The martin boundary of a free product of abelian groups
• Local limit theorem for symmetric random walks in Gromov-hyperbolic groups
• Projections and relative hyperbolicity
• Phase Transitions for Random Walk Asymptotics on Free Products of Groups

Related

• A local limit theorem for convergent random walks on relatively hyperbolic groups
• Local limit theorems in relatively hyperbolic groups II : the non-spectrally degenerate case
• Local limit theorems in relatively hyperbolic groups I : rough estimates
• Local limit theorem for symmetric random walks in Gromov-hyperbolic groups
• Local limit theorem for random walks on symmetric spaces