The Structure of Extreme Level Sets in Branching Brownian Motion

Understand

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.