Mathematics Colloquium - Gabriel Leite Baptista da Silva University of Groningen

Title: The Contact Process over a Dynamical d-regular Graph

Abstract:

The contact process on a random d-regular graph survives for a time that is exponential on the number of vertices when the infection rate is larger than a threshold value: the critical rate for survival of the contact process on the d-regular tree. We study the contact process on a dynamic graph defined as a random d-regular graph with a stationary edge-switching dynamics. We prove that if the infection rate of the contact process is above a threshold value (depending on d and v), then the infection survives for a time that grows exponentially with the size of the graph. By proving that this threshold is strictly smaller than the lower critical infection rate of the contact process on the infinite d-regular tree, we show that there are values of the infection rate for which the infection dies out in logarithmic time in the static graph but survives exponentially long in the dynamic graph.

Joint work with Prof. Roberto Oliveira (IMPA) and Prof. Daniel Valesin (Warwick).