论文标题
两个BBM领导者之间的距离
The distance between the two BBM leaders
论文作者
论文摘要
我们研究布朗尼分支运动中两个最右边粒子之间的距离。德里达（Derrida）和第二作者表明，该随机变量的长期限制$ d_ {12} $可以用与Fisher-kpp方程相关的PDE表示。我们使用这样的表示形式来确定$ \ mathbb {p}（d_ {12}> a）$的尖锐渐近差为$ a \ to+\ infty $。这些尾巴渐近学以前是“指数级”的；我们发现对此行为的代数校正。
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 $\mathbb{P}(d_{12} > a)$ as $a\to+\infty$. These tail asymptotics were previously known to "exponential order;" we discover an algebraic correction to this behavior.
