We provide equivalent conditions for Liouville property of actions of groups. As an application, we show that there is a Liouville measure for the action of the Thompson group F on dyadic rationals. This result should be compared with a recent result of Kaimanovich, where he shows that the action of the Thompson group F on dyadic rationals is not Liouville for all finitely supported measures. As another application we show that there is a Liouville measure for lamplighter actions. This gives more examples of non-amenable Liouville actions.
Classification :
60-XX, 43-XX
Mots-clés :
Liouville property, amenability, Schreier graph, Thompson group F
Affiliations des auteurs :
Kate Juschenko
1
;
Tianyi Zheng
2
1
Northwestern University, Evanston, USA
2
University of California San Diego, La Jolla, USA
Kate Juschenko; Tianyi Zheng. Infinitely supported Liouville measures of Schreier graphs. Groups, geometry, and dynamics, Tome 12 (2018) no. 3, pp. 911-918. doi: 10.4171/ggd/464
@article{10_4171_ggd_464,
author = {Kate Juschenko and Tianyi Zheng},
title = {Infinitely supported {Liouville} measures of {Schreier} graphs},
journal = {Groups, geometry, and dynamics},
pages = {911--918},
year = {2018},
volume = {12},
number = {3},
doi = {10.4171/ggd/464},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/464/}
}
TY - JOUR
AU - Kate Juschenko
AU - Tianyi Zheng
TI - Infinitely supported Liouville measures of Schreier graphs
JO - Groups, geometry, and dynamics
PY - 2018
SP - 911
EP - 918
VL - 12
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/464/
DO - 10.4171/ggd/464
ID - 10_4171_ggd_464
ER -
