Speaker: 林棽，Sorbonne Université

Inviter: 随机分析研究中心

Title: Yaglom theorem for critical branching random walk on $Z^d$

Language: Chinese

Time & Venue: 2026.04.17 15:00-16:00 南楼N613

Abstract: We study the critical branching random walk on $Z^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $Z^d$. We are interested in the occupation time in $K$ and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order $\|x\|^{4-d}$ in dimensions $d\leq 3$, of order $\log \|x\|$ in dimension $d=4$, and of order $1$ in dimensions $d\geq 5$. The corresponding weak convergences are also established. These results answer a question raised by Le Gall and Merle (Elect. Comm. in Probab. 11 (2006), 252–265). This is a joint work with Xinxin Chen (Beijing Normal University), available at https://arxiv.org/abs/2512.24047.