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Isaac Newton Institute for Mathematical Sciences

Asymptotic aspects of Schreier graphs of self-similar groups

26th January 2007

Author: Sunik, Z (Texas A&M)

Abstract

We consider Schreier graphs of actions of self-similar groups and present relations between their asymptotic properties, such as volume growth, growth of diameters, rate of vanishing of the spectral gap, etc. Among the examples illustrating the possible types of behavior we consider Hanoi Towers groups, Baumslag-Solitar groups, lamplighters, Basilica group, Bellaterra group, etc.