Branching number of a graphed pseudogroup

Samedi 1er janvier 1994 15:30-00:00 - Perez Fernandez de Cordoba Maria - University Santiago de Compostela

Résumé : Lyons has defined an average number of branches per vertex of an infinite locally finite rooted tree. This number has an important role in several probabilistic processes such as random walk and percolation. We extend the notion of branching number to any measurable graphed pseudogroup of finite type acting on a probability space.
We prove that such a pseudogroup is amenable if its branching number is equal to 1. In order to prove that this actually generalizes results of C. Series and V. Kaimanovich on equivalence relations with polynomial and subexponential growth, we describe an example of minimal lamination whose holonomy pseudogroup has branching number 1 and exponential growth.

Lieu : 425 - 113-115

Branching number of a graphed pseudogroup  Version PDF