数学研究所

中国科学院华罗庚数学重点实验室

学术报告

         多复变与复几何研讨班

                         SCV&CG Seminar

Speaker: 陈昕昕 教授 (北京师范大学)

Language: Chinese

Title: Classical critical branching processes, Kolmogorov estimate and Yaglom theorem

Time&Venue: 2025.02.25（星期二）15:30-17:00

& 思源楼S813

Abstract: We consider a critical Galton-Watson process (Zn), n>0, which get extinct a.s. Kolmogorov estimate gives the decaying order of P(Zn > 0). Yaglom theorem means that conditioned on Zn > 0, Zn/n converges in law to some exponential distribution. We talk about a new proof via Stein method for these classical results.

Title：Critical branching random walk in i.i.d. random envrionment

Time&Venue:2025.02.26（星期三）15:30-17:00 

&思源楼713

Abstract:We consider a branching random walk in random environment where the environment is given by Bernoulli site percolation. At closed site, the particles branch according to critical (0, 2) law, while at open site, the particles do not branch. We establish quenched Kolmogorov estimate and Yaglom theorem for this model, which solve a conjecture of Englander and Peres.

Title：Critical branching random walk in Z^4: hitting probability and occupation time

Time&Venue:2025.02.27（星期四）15:30-17:00

&思源楼813

Abstract:We consider a branching random walk in Z^4 started from some far away x. We talk about the asymptotic of the probability that this process hits the origin and link this problem with Kolmogorov estimate. Moreover, we give the convergence in law of occupation time at the origin conditioned on hitting the origin, which is also viewed as a Yaglom theorem.