報(bào)告人：張樹(shù)雄 博士

報(bào)告題目：On the empty balls of branching random walks

報(bào)告時(shí)間：2025年11月8日（周六）上午10：45

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

張樹(shù)雄，安徽師范大學(xué)講師，2021年博士畢業(yè)于北京師范大學(xué)，2021-2023于南方科技大學(xué)開(kāi)展博士后研究，研究方向?yàn)闇y(cè)度值分支過(guò)程及相關(guān)領(lǐng)域，研究成果發(fā)表在Bernoulli,ECP,JTP,JAP 等期刊，現(xiàn)主持國(guó)家自然科學(xué)基金青年項(xiàng)目1項(xiàng)，參與重點(diǎn)研發(fā)計(jì)劃項(xiàng)目與面上項(xiàng)目各1項(xiàng)。

報(bào)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.