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The Structure of Extreme Level Sets in Branching Brownian Motion

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Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. Arguin et al.\ and A\”\i{}d\’ekon et al.\ proved the convergence of the extremal process. In the talk we discuss how one can obtain finer results on the extremal level sets by using a random walk-like representation of the extremal particles. We establish among others the asymptotic density of extremal particles at a given distance from the maximum and the upper tail probabilities for the distance between the maximum and the second maximum (joint work with Aser Cortines and Oren Louidor).

This talk is part of the Probability series.

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