Title: The contact process on random graphs

Abstract: The contact process is a model of infections on networks. We will establish phase transitions for the contact process on the Erdos–Renyi and other random graphs. Answering a question of Huang and Durrett we show that the critical infection rate $\lambda_1$ for weak survival on a branching process is strictly positive if and only if the distribution has some finite exponential moment. Analogous results hold for random graphs with given degree distributions. 

*Joint work with Shankar Bhamidi, Danny Nam, and Oanh Nguyen.