The distance between the two BBM leaders

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 s...

Ամբողջական նկարագրություն

Մատենագիտական մանրամասներ
Հիմնական հեղինակներ: Berestycki, J, Brunet, E, Graham, C, Mytnik, L, Roquejoffre, J-M, Ryzhik, L
Ձևաչափ: Journal article
Լեզու:English
Հրապարակվել է: IOP Publishing 2022
Նկարագրություն
Ամփոփում: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.