Amenability and Unique Ergodicity of Automorphism Groups of Fraïssé Structures

2013/04/10 by Zucker, Andy
#37B05 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Probability (math.PR)

paper · doi:10.48550/arxiv.1304.2839

Abstract

In this paper we provide a necessary and sufficient condition for the amenability of the automorphism group of Fraïssé structures and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the Boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering GL(V_∞), where V_∞ is the countably infinite dimensional vector space over a finite field F_q, we show that the unique invariant measure on the universal minimal flow of GL(V_∞) is not supported on the generic orbit.

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