搜索:
 
 当前位置:>首页 -> 学术报告
6-16天元基金几何与随机分析及其应用交叉讲座之117【何辉】

报告题目:On large deviation probabilities for empirical distribution of branching random walks: Schroder case and Bottcher case

报告人:何辉,北京师范大学 

时间:2018616日 上午9:00-10:00

地点:管研楼1518

摘要:

Given a super-critical branching random walk on $\mathbb R$ started from the origin, let $Z_n(\cdot)$ be the counting measure which counts the number of individuals at the $n$-th generation located in a given set. Under some mild conditions, it is known  that for any interval $A\subset {\mathbb R}$, $\frac{Z_n(\sqrt{n}A)}{Z_n({\mathbb R})}$ converges a.s. to $\nu(A)$,  where $\nu$ is the standard Gaussian measure.In this work, we investigate the convergence rates of $${\mathbb P}\left(\frac{Z_n(\sqrt{n}A)}{Z_n({\mathbb R})}-\nu(A)>\Delta\right),$$ for $\Delta\in (0, 1-\nu(A))$, in both Schr\"{o}der case and B\"{o}ttcher case. This is a joint work with Xinxin Chen.
  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会