报告人：薛晓峰（北京交通大学）

报告题目：Limit theorems of occupation times of normalized binary contact path processes on lattices

报告摘要：The binary contact path process (BCPP) introduced in Griffeath (1983) describes the spread of an epidemic on a graph and is an auxiliary model in the study of improving upper bounds of the critical value of the contact process. In this talk, we are concerned with limit theorems of the occupation time of a normalized version of the BCPP (NBCPP) on a lattice. We first show that the law of large numbers of the occupation time process is driven by the identity function when the dimension of the lattice is at least 3 and the infection rate of the model is sufficiently large conditioned on the initial state of the NBCPP being distributed with a particular invariant distribution. Then we show that the centered occupation time process of the NBCPP converges in finite dimensional distributions to a Brownian motion when the dimension of the lattice and the infection rate of the model are sufficiently large and the initial state of the NBCPP is distributed with the aforementioned invariant distribution.

报告时间：2024年6月6日（星期四）14:30-16:00

报告地点：东三十二楼115室

邀请人：赵林杰

报告人简介：薛晓峰，北京交通大学副教授。研究领域为交互作用粒子系统和图上的马氏过程，以往工作主要研究接触过程的临界值估计、流体动力学极限以及中偏差等问题，在Journal of Statistical Physics, Electronic Journal of Probability, Stochastic Processes and their Applications, Potential Analysis等杂志发表论文三十余篇。