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### Competition processes on hyperbolic non-amenable graphs

**Probability**

Speaker: | Elisabetta Candellero, Roma Tre University |

Location: | MSB 2112 |

Start time: | Tue, Apr 18 2023, 1:10PM |

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.