The distance between the two BBM leaders-Reference-Cited by-同舟云学术

The distance between the two BBM leaders

Published:2022-02-16 Issue:4 Volume:35 Page:1558-1609
ISSN:0951-7715
Container-title:Nonlinearity
language:
Short-container-title:Nonlinearity

Author:

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

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

a)$?>

P ( d 12 > a )

as a → +∞. These tail asymptotics were previously known to ‘exponential order;’ we discover an algebraic correction to this behavior.

Publisher

IOP Publishing

Subject

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

Link

https://iopscience.iop.org/article/10.1088/1361-6544/ac4a8e/pdf

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