A non-symmetric Kesten criterion for random walks on groups

Richard Sharp (U Warwick)

Jul 19. 2023, 09:00 — 09:45

A famous result of Kesten from 1959 relates symmetric random walks on countable groups to amenability. Precisely, provided the support of the walk generates the group, the probability of return to the identity in 2n steps decays exponentially fast if and only if the group is not amenable. This led to many analogous “amenability dichotomies”, for example for the spectrum of the Laplacian of manifolds and critical exponents of discrete groups of isometries. I will present a version of the dichotomy for non-symmetric walks. This is joint work with Rhiannon Dougall.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)