Título: Renewal Contact Process: phase transition and survival

Palestrante: Daniel Ungaretti (IME-USP)
Data: 04/01/2021
Horario: 15:00 - 16:00 (Horário do Rio de Janeiro)
Local: Transmissão Online

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Resumo: The Contact Process was introduced by Harris in 1974 and models the spread of an infection on a graph. The state of each vertex is either infected or healthy, and there are two competing factors that govern the evolution of the process over time: infected vertices become healthy at rate 1 and healthy vertices can get infected at a rate proportional to its current number of infected neighbors. In two recent papers, Fontes, Marchetti, Mountford and Vares introduced a generalization of the model in which cures are given by renewal processes with some fixed interarrival distribution. I will discuss how the choice of interarrival distribution affects the spread of the infection, focusing on recent developments in which we improved the characterization of the interarrival distributions for which there is phase transition. Joint work with Luiz Renato Fontes, Tom Mountford and Maria Eulália Vares.