Limit sets for branching random walks on relatively hyperbolic groups

Abstract

Branching random walks (BRW) on groups consist of two independent processes on the Cayley graphs: branching and movement. Start with a particle on a favorite location of the graph. According to a given offspring distribution, the particles at the time n split into a random set of particles with mean $r \ge 1$, each of which then moves independently with a fixed step distribution to the next locations. It is well-known that if the offspring mean $r$ is less than the spectral radius of the underlying random walk, then BRW is transient: the particles are eventually free on any finite set of locations. The particles trace a random subgraph which accumulates to a random subset called limit set in a boundary of the graph. In this talk, we consider BRW on relatively hyperbolic groups and study the limit set of the trace at the Bowditch and Floyd boundaries. In particular, the Hausdorff dimension of the limit set will be computed. This is based on a joint work with Mathieu Dussaule and Longmin Wang

Speaker

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https://bicmr.pku.edu.cn/~wyang/