The distance between the two BBM leaders. (7th April 2022)

• Record Type: Journal Article
• Authors: Berestycki, Julien; Brunet, Éric; Graham, Cole; Mytnik, Leonid; Roquejoffre, Jean-Michel; Ryzhik, Lenya
• Is Part Of: Nonlinearity. Volume 35:Number 4(2022)
• Page Start: 1558
• Page End: 1609
• Publication Date: 2022-04-07
• Subjects: branching Brownian motion -- Fisher–KPP equation -- branching processes; 35K57 -- 60J80; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac4a8e
• Languages: English
• ISSNs: 0951-7715

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.