Stationary random graphs and groups

Abstract: A stationary random graph is a random rooted graphs $(G,o)$ such that replacing the root $o$ by its random neighbor results in the same probability distribution. The more well known unimodular random graphs are always stationary, but the unimodularity assumption is in fact much stronger. Invariant random subgroups and unimodular random graphs are now a household name in measured group theory, and they found several applications in geometry and topology. In my talk I want to advertise and describe some applications of the stationary random graphs and groups. I will explain how they can be used to find non-expander sub-graphs inside any given graph and how to prove that any higher rank locally symmetric space of infinite volume must have points of arbitrary large injectivity radius. The talk is based on a joint work with Wouter Van Limbeek and with Tsachik Gelander.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.