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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.
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Submitted on : Monday, May 16, 2022 - 2:43:09 PM
Last modification on : Monday, July 4, 2022 - 9:48:44 AM

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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, IOP Publishing, 2022, 35 (4), pp.1558-1609. ⟨10.1088/1361-6544/ac4a8e⟩. ⟨hal-03669216⟩

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