Abstract
We construct measures invariant with respect to equivalence relations which are graphed by horospheric products of trees. The construction is based on using conformal systems of boundary measures on treed equivalence relations. The existence of such an invariant measure allows us to establish amenability of horospheric products of random trees.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1203.37013
MathSciNet: MR2648261
Digital Object Identifier: 10.2969/aspm/05710199
Subjects:
Primary:
37A20
Secondary:
05C80
,
43A07
,
60J80
Keywords:
amenability
,
branching process
,
graphed equivalence relation
,
Horospheric product
,
Random tree
,
Stochastic homogenization
Rights: Copyright © 2010 Mathematical Society of Japan
