Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 199 - 229
Stochastic homogenization of horospheric tree products
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.
Received: 13 May 2009
First available in Project Euclid: 24 November 2018
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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.)
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. https://projecteuclid.org/euclid.aspm/1543086320