Competition processes on hyperbolic non-amenable graphs.

Abstract: 

We consider two first-passage percolation processes, FPP_1 and FPP_\lambda, spreading with rates 1 and \lambda  respectively, on a graph G with bounded degree.  FPP_1 starts from a single source, while the initial configuration of FPP_\lambda consists of countably many seeds distributed according to a product of iid Bernoulli random variables of parameter \mu on the set of vertices.

This model is known as “First passage percolation in a hostile environment” (FPPHE), it was introduced by Stauffer and Sidoravicius as an auxiliary model for investigating a notoriously challenging model called Multiparticle Diffusion Limited Aggregation.  We consider several questions about FPPHE, focusing on the case where G is a non-amenable hyperbolic graph. This talk is based on joint works with Alexandre Stauffer.

Posted on May 2, 2022 in Seminario de Probabilidades de Chile, Seminars