ABSTRACT OF THE TALK
The contact process is a classical interacting particle system which models the spread of a disease inside a network. For bounded degree graphs, there always exists a positive critical infection rate below which the infection vanishes almost-surely. On the other hand, if the graph has unbounded degree, it may happen that the infection survives for any infection rate. In this talk, I will define a percolation model on the vertices of the graph called "cumulatively merged partition". I will try to explain how the existence of an infinite cluster relates to the existence of a sub-critical infection phase for the contact process. Based on a joint work with L. Ménard.
BIOGRAPHY
Arvind Singh is a researcher at the French National Center for Scientific Research, affiliated with the Mathematics Department of University Paris-Sud. He graduated from École Normale Supérieure in Paris and subsequently obtained a Ph.D. from University Paris 6, under the supervision of Prof. Yueyun Hu. His research interests focus on Probability theory and include topics such as random walks, random media, interacting particles systems and other related models of statistical physics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai