Kesten's criterion for discrete probability measure-preserving groupoids

TL;DR

This paper extends Kesten's criterion from groups to discrete probability measure-preserving groupoids, characterizing their amenability via operator norms of symmetric invariant Markov operators.

Contribution

It introduces a new criterion for amenability of groupoids based on operator norm conditions, generalizing Kesten's criterion from groups to groupoids.

Findings

Characterization of groupoid amenability using operator norms

Extension of Kesten's criterion to groupoids

New analytical tools for studying groupoid properties

Abstract

Inspired by Kesten's criterion for the amenability of groups, we establish a characterization of the amenability of discrete probability measure-preserving groupoids in terms of the operator norms of symmetric invariant Markov operators.