Advanced Studies in Pure Mathematics

Stochastic homogenization of horospheric tree products

Vadim A. Kaimanovich and Florian Sobieczky

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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.

Article information

Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 199-229

Received: 13 May 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document euclid.aspm/1543086320

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 05C80: Random graphs [See also 60B20] 43A07: Means on groups, semigroups, etc.; amenable groups 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Horospheric product random tree branching process graphed equivalence relation stochastic homogenization amenability


Kaimanovich, Vadim A.; Sobieczky, Florian. Stochastic homogenization of horospheric tree products. Probabilistic Approach to Geometry, 199--229, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710199.

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