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