Probability Seminar——Hydrodynamic limits and fluctuations of binary contact path processes
报告人：Xiaofeng Xue(Beijing Jiaotong University)
时间：2021-3-22 14:00-15:00
地点：Room 1114, Sciences Building No. 1
Abstract: The binary contact path process describes the spread of an epidemic on a graph, where an infectious vertex recovers at rate 1 while a healthy vertex x is infected by an infectious neighbor y at an infection rate λ. When y infects x, the seriousness η(x) of the ill of x is added with that of y . The binary contact path process is an auxiliary model to give upper bound of the critical value of the contact process and belongs to a large family of stochastic processes called `linear systems' introduced in Section 9 of Liggett's IPS book published in 1985. In this talk, we will introduce our results about hydrodynamic limits and fluctuations of binary contact path processes on Zd with d and λ sufficiently large. We show that the hydrodynamic limit is driven by the weak solution of a heat equation while the fluctuation is driven by a generalized O-U process. The key step of the proofs is to bound the fourth moment of η(x). This talk is based on joint works with Dr. Linjie Zhao.
