Probability Seminar

Date: November 16, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Luiz Renato Fontes, University of Sao Paulo and NYU Shanghai

Title: Contact processes with general inter-recovery times

Abstract: We study the contact process in d dimensions with the usual exponential infection times, of rate lambda, but with general recovery times, rather than just the usual exponential recovery times. We seek conditions on the common distribution F of the recovery times in order to have survival (of the infection, with positive probability) for either 1) all λ>0; or 2) only for λ large enough. Regarding 1), such a condition is that F satisfies some regularity conditions evocative of, but going considerably beyond, inclusion in the basin of attraction of a stable law with index less than 1. And 2) holds if a) F has two moments (by a standard, simple argument); or (more involvedly) if b) F has a greater than 1 moment and (for technical reasons) d = 1, and also F has a decreasing hazard rate. We will introduce the model and results in detail, and explain the main ideas and steps in our proofs. Joint work with Domingos Marchetti, Tom Mountford and Maria Eulália Vares.