報告人：張樹雄 博士

報告題目：On the empty balls of branching random walks

報告時間：2025年11月8日（周六）上午10：45

報告地點：云龍校區6號樓304會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

張樹雄，安徽師范大學講師，2021年博士畢業于北京師范大學，2021-2023于南方科技大學開展博士后研究，研究方向為測度值分支過程及相關領域，研究成果發表在Bernoulli,ECP,JTP,JAP 等期刊，現主持國家自然科學基金青年項目1項，參與重點研發計劃項目與面上項目各1項。

報告摘要：

Let R_n be the radius of the largest empty ball centered at the origin of a branching random walk started from a Poisson random measure at time n. In 2002, Revesz proved that for a 1-dimensional critical branching Wiener process, R_n/n converges in law. For d=2 and d>2, he conjectured that R_n/\sqrt n and R_n will converge in law, respectively. Later, Hu confirmed the case of d>2 in 2005. In this talk, we intend to prove the case of d=2 in a general setting. Moreover, we shall also deal with some new cases eg. the offspring law is subcritical or the offspring law has infinite variance, etc. Part of the work comes from the cooperation with Prof. Jie Xiong.