分支随机游动顶点的统计与行波的时滞
Statistics at the tip of a branching random walk and the delay of traveling waves
摘要：
研究了分支随机游动边界粒子的极限分布。这些粒子的位置可以被看作是在平均场的情况下，在随机介质中的定向聚合物的最低能量。我们表明，这些领先的粒子之间的平均距离可以计算为行波的延迟根据Fisher-KPP波前方程的演变。这些平均距离表现出普遍的行为，不同于最近在平均场自旋玻璃的背景下研究的概率级联。
英文摘要：
We study the limiting distribution of particles at the frontier of a branching random walk. The positions of these particles can be viewed as the lowest energies of a directed polymer in a random medium in the mean-field case. We show that the average distances between these leading particles can be computed as the delay of a traveling wave evolving according to the Fisher-KPP front equation. These average distances exhibit universal behaviors, different from those of the probability cascades studied recently in the context of mean field spin-glasses.
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