EVENT DETAILS AND ABSTRACT

Title: Extreme Level Sets of Branching Brownian Motion
Speaker: Lisa Hartung
Speaker Info: Courant Institute
Brief Description:
Special Note:
Abstract:

We study the structure of extreme level sets of a standard one dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height and shape of those clusters which carry such level sets. We also find the right tail decay of the distribution of the distance between the two highest particles. These results confirm two conjectures of Brunet and Derrida.(joint work with A. Cortines, O Louidor) If time permits I will explain a second approach to get a better understanding of the extremal particles using the connection between the F-KPP equation and branching Brownian motion.