# More on the Structure of Extreme Level Sets in Branching Brownian Motion

## TL;DR

This paper investigates the detailed structure of particles near the maximum in branching Brownian motion, revealing that a small number of unusually large clusters dominate the extreme level sets.

## Contribution

It extends previous work by showing that most particles in extreme level sets originate from a few atypically large clusters.

## Key findings

- Most particles in extreme level sets come from a small fraction of large clusters.
- Large clusters are atypically big and dominate the extreme level sets.
- The structure of extreme level sets is heavily influenced by these large clusters.

## Abstract

This work is a continuation of the manuscript "the structure of extreme level sets in branching Brownian motion", in which the same authors studied the fine structure of the extreme level sets of branching Brownian motion, namely the sets of particles whose height is within a finite distance from 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. Our main finding here is that most of the particles in an extreme level set come from only a small fraction of the clusters, which are atypically large.