The distance between the two BBM leaders

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...

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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.

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