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Journal Articles Nonlinearity Year : 2022

The distance between the two BBM leaders

Abstract

Abstract We study the distance between the two rightmost particles in branching Brownian motion. Derrida and the second author have shown that the long-time limit d 12 of this random variable can be expressed in terms of PDEs related to the Fisher–KPP equation. We use such a representation to determine the sharp asymptotics of P ( d 12 > a ) as a → +∞. These tail asymptotics were previously known to ‘exponential order;’ we discover an algebraic correction to this behavior.

Dates and versions

hal-03669216 , version 1 (16-05-2022)

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Julien Berestycki, Éric Brunet, Cole Graham, Leonid Mytnik, Jean-Michel Roquejoffre, et al.. The distance between the two BBM leaders. Nonlinearity, 2022, 35 (4), pp.1558-1609. ⟨10.1088/1361-6544/ac4a8e⟩. ⟨hal-03669216⟩
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