Amenability of trees
Behrang Forghani, Keivan Mallahi-Karai

TL;DR
This paper establishes a criterion for determining when locally finite trees are amenable, using a novel trimming operator, and applies it to characterize amenability in Galton-Watson trees.
Contribution
It introduces a new criterion based on a trimming operator for assessing amenability of trees, including Galton-Watson trees.
Findings
Criterion for amenability of locally finite trees
Necessary and sufficient condition for Galton-Watson trees
Introduction of a trimming operator for trees
Abstract
We will give a criterion for the amenability of arbitrary locally finite trees. The criterion is based on the trimming operator which is defined on the space of trees. As an application, we obtain a necessary and sufficient condition for that amenability of Galton-Watson trees.
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Taxonomy
TopicsStochastic processes and statistical mechanics
