The distance between the two BBM leaders

Julien Berestycki; Éric Brunet; Cole Graham; Leonid Mytnik; Jean Michel Roquejoffre; Lenya Ryzhik

doi:10.1088/1361-6544/ac4a8e

The distance between the two BBM leaders

Julien Berestycki, Éric Brunet, Cole Graham, Leonid Mytnik, Jean Michel Roquejoffre, Lenya Ryzhik

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

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 a)$?> P(d12>a) as a → +∞. These tail asymptotics were previously known to 'exponential order;' we discover an algebraic correction to this behavior.

Original language	English
Pages (from-to)	1558-1609
Number of pages	52
Journal	Nonlinearity
Volume	35
Issue number	4
DOIs	https://doi.org/10.1088/1361-6544/ac4a8e
State	Published - Apr 2022

Keywords

35K57
60J80
branching Brownian motion
branching processes
Fisher-KPP equation

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/ac4a8e

Cite this

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title = "The distance between the two BBM leaders",

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 a)$?> P(d12>a) as a → +∞. These tail asymptotics were previously known to 'exponential order;' we discover an algebraic correction to this behavior.",

keywords = "35K57, 60J80, branching Brownian motion, branching processes, Fisher-KPP equation",

author = "Julien Berestycki and {\'E}ric Brunet and Cole Graham and Leonid Mytnik and Roquejoffre, {Jean Michel} and Lenya Ryzhik",

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AU - Berestycki, Julien

AU - Brunet, Éric

AU - Graham, Cole

AU - Mytnik, Leonid

AU - Roquejoffre, Jean Michel

AU - Ryzhik, Lenya

PY - 2022/4

Y1 - 2022/4

N2 - 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 a)$?> P(d12>a) as a → +∞. These tail asymptotics were previously known to 'exponential order;' we discover an algebraic correction to this behavior.

AB - 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 a)$?> P(d12>a) as a → +∞. These tail asymptotics were previously known to 'exponential order;' we discover an algebraic correction to this behavior.

KW - 35K57

KW - 60J80

KW - branching Brownian motion

KW - branching processes

KW - Fisher-KPP equation

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VL - 35

SP - 1558

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JO - Nonlinearity

JF - Nonlinearity

IS - 4

ER -

The distance between the two BBM leaders

Abstract

Keywords

ASJC Scopus subject areas

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