The distance between the two BBM leaders. (7th April 2022) - Berestycki, Julien; Brunet, Éric; Graham, Cole; Mytnik, Leonid; Roquejoffre, Jean-Michel; Ryzhik, Lenya
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.