Probability Seminar
Thursday, September 12, 2019, 3:15pm, 119 Physics
Danny Nam (Princeton)
The contact process on random trees and graphs

Abstract:

The contact process describes an elementary epidemic model, where each infected site gets healed at rate 1 while it passes its disease to each of its neighbors independently at rate \lambda. In this talk, we show that the phase diagram of the contact process on a Galton-Watson tree depends on the tail of the offspring distribution in the following sense: the extinction-survival threshold is strictly positive if and only if the tail has an exponential decay. In such cases, we further achieve the first-order asymptotics for the location of the threshold. We will also discuss analogous results for Erdos–Renyi and other random graphs. Joint work with Shankar Bhamidi, Oanh Nguyen and Allan Sly.

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