ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK  

作　　者：Shuxiong ZHANG Jie XIONG 张树雄;熊捷(School of Mathematics and Statistics,Anhui Normal University,Wuhu,241002,China;Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China)

机构地区：[1]School of Mathematics and Statistics,Anhui Normal University,Wuhu,241002,China [2]Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

出　　处：《Acta Mathematica Scientia》2024年第5期2051-2072,共22页数学物理学报（B辑英文版）

基　　金：supported by the National Key R&D Program of China(2022YFA1006102).

摘　　要：Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

关 键 词：empty ball DIMENSION branching random walk super-Brownian motion 

分 类 号：O211.6[理学—概率论与数理统计]