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Probability and Combinatorics

Tuesday, April 16, 2024 - 3:30pm

Yujin Kim

NYU Courant


Temple University

Wachman Hall 617

The extremal process of branching Brownian motion (BBM) —i.e., the collection of particles furthest from the origin— has gained lots of attention in dimension d=1 due to its significance to the universality class of log-correlated fields, as well as to certain PDEs. In recent years, a description of the extrema of BBM in d>1 has been obtained. In this talk, we address the following geometrical question that can only be asked in d>1. Generate a BBM at a large time, and draw the outer envelope of the cloud of particles: what is its shape? Macroscopically, the shape is known to be a sphere; however, we focus on the outer envelope around an extremal point— the "front" of the BBM. We describe the scaling limit for the front, with scaling exponent 3/2, as an explicit, rotationally-symmetric random surface. Based on joint works with Julien Berestycki, Bastien Mallein, Eyal Lubetzky, and Ofer Zeitouni.