SEMINARIO Probabilita'

Daniel Valesin (University of Groningen)

Titolo: On the threshold of spread-out contact process percolation

Lunedi' 04 Novembre 2019 ORE 16:30

Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1 - Pal.C - Aula 211

Abstract We study the stationary distribution of the (spread-out) d-dimensional contact process from the point of view of site percolation. In this process, vertices of ^d can be healthy (state 0) or infected (state 1). With rate one infected individuals recover, and with rate lambda they transmit the infection to some other vertex chosen uniformly within a ball of radius R. The classical phase transition result for this process states that there is a critical value lambda_c(R) such that the process has a non-trivial stationary distribution if and only if lambda > lambda_c(R). In configurations sampled from this stationary distribution, we study nearest-neighbor site percolation of the set of infected sites; the associated percolation threshold is denoted lambda_p(R). We prove that lambda_p(R) converges to 1/(1-p_c) as R tends to infinity, where p_c is the threshold for Bernoulli site percolation on ^d. As a consequence, we prove that lambda_p(R) > lambda_c(R) for large enough R, answering an open question of [Liggett, Steif, AIHP, 2006] in the spread-out case. Joint work with Bala'zs Ra'th.

Alexandre