Título: On the threshold of spread-out contact process percolation
Palestrante: Daniel Valesin (University of Groningen)

Data: 27 de julho de 2020 (segunda-feira)
Hora: 15:00 h

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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 \Z^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 \Z^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 Balázs Ráth.

Organizadores: Guilherme Ost e Maria Eulalia Vares