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：2018年6月16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.