Agenda de l’IDP

Séminaire SPACE Tours

Ends of the trace of branching random walks on groups
Lorenz Gilch (Technische Universität Graz)
Friday 07 November 2014 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
In this talk we will consider discrete-time branching random walks on the Cayley graph of hyperbolic groups and free products of groups, which can be described in the following way. An initial particle starts at the identity. At each instant of time, each particle produces in a first stage some offspring according to an offspring distribution and in a second stage each of the offspring particles moves independently to a neighbour element in the group. That is, each particle performs its own independent single random walk from its place of birth. We investigate the phase of branching random walks, where the branching process survives and where the process vacates each finite subset almost surely after finite time. The trace is then the subgraph of visited vertices and edges. The purpose of this talk is to describe the boundary of the trace. In the case of free products we summarize some results, which describe the set of ends of the Cayley graph of the free product, where the branching random walk accumulates. In the case of one-ended planar, hyperbolic groups a recent result (joint work with Sebastian Müller) will be presented: the trace has uncountably many ends and no isolated end.

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