Amenability and unique ergodicity of automorphism groups of Fraïssé structures

Andy Zucker. "Amenability and unique ergodicity of automorphism groups of Fraïssé structures." Fundamenta Mathematicae 226.1 (2014): 41-61. <http://eudml.org/doc/286626>.

@article{AndyZucker2014,
abstract = {In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable 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.},
author = {Andy Zucker},
journal = {Fundamenta Mathematicae},
keywords = {Fraïssé theory; Ramsey theory; universal minimal flow; amenability; unique ergodicity},
language = {eng},
number = {1},
pages = {41-61},
title = {Amenability and unique ergodicity of automorphism groups of Fraïssé structures},
url = {http://eudml.org/doc/286626},
volume = {226},
year = {2014},
}

TY - JOUR
AU - Andy Zucker
TI - Amenability and unique ergodicity of automorphism groups of Fraïssé structures
JO - Fundamenta Mathematicae
PY - 2014
VL - 226
IS - 1
SP - 41
EP - 61
AB - In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable 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.
LA - eng
KW - Fraïssé theory; Ramsey theory; universal minimal flow; amenability; unique ergodicity
UR - http://eudml.org/doc/286626
ER -