The contact process is a continuous-time Markov process describing the spread of an epidemic on a graph, where each infectious vertex is recovered at a constant rate while each healthy one is infected at rate proportional to infectious neighbors. This model performs many important phenomena such as phase transition, monotonicity, self-duality and so on and hence is a popular topic in the study of discrete probability theory since it was introduced by T. Harris in 1974.  In this talk, we will first briefly review some basic properties of contact processes and then introduce some of our recent works about asymptotic behaviors of contact processes on high-dimensional lattices.

Xiao-Feng Xue is an associate professor at School of Science, Beijing Jiaotong University since 2018. He was a post-doc at University of Chinese Academy of Sciences, from 2014 to 2016. He obtained his PhD degree from Peking University in 2014. His primary research interests are in interacting particle systems and Markov processes on graphs.