Extreme level sets of branching Brownian motion and friends
随机研究中心学术短课
报告题目(Title)：Extreme level sets of branching Brownian motion and friends
报告人(Speaker)：Lisa Hartung (Johannes Guttenberg University, Germany )
地点(Place)：后主楼12层 1220
时间(Time)：7月22，23，25，26号 10:00-12:00
邀请人(Inviter)：何辉
报告摘要
Branching Brownian motion (BBM) is a classical process in probability theory, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. It also belongs the class of so called log-correlated random fields. We will focus on the behaviour of the extremal particles of BBM.
First, we will understand how the correlations in the model effect the order of the maximum. Then, I will explain why the extremal process of BBM converges to a random cluster process. Building on these known results, we will move on to recent result on the extreme level sets of BBM. We find the asymptotic size of extreme level sets and the typical height and shape of those clusters which carry such level sets. I will explain how truncated moments help to reduce questions on the size / shape of extreme level sets to random walk like estimates.
I will also explain which models are conjectured to fall in the same universality class as BBM and explain what has been proven rigorously
