论文标题
无限步行者系统：获胜者和失败者
Infinite System of Random Walkers: Winners and Losers
论文作者
论文摘要
我们研究了一个无限的粒子系统，最初占据了半线$ y \ leq 0 $，并在整个生产线上进行随机步行。最正确的粒子称为领导者。令人惊讶的是，除原始领导者以外的每个粒子都可能永远无法在整个演变中取得领导地位。对于等距初始配置，$ k^{\ text {th}} $粒子具有概率$ e^{ - 2} k^{ - 1}（\ ln k）^{ - 1/2} $时$ k \ k \ gg gg 1 $。这提供了对早期不幸（以$ k $表示）与永恒失败之间相关性的定量度量。我们还表明，定义为第一个沃克的获胜者超过了初始领导者的标签$ k \ gg 1 $，概率衰减为$ \ exp \！\！
We study an infinite system of particles initially occupying a half-line $y\leq 0$ and undergoing random walks on the entire line. The right-most particle is called a leader. Surprisingly, every particle except the original leader may never achieve the leadership throughout the evolution. For the equidistant initial configuration, the $k^{\text{th}}$ particle attains the leadership with probability $e^{-2} k^{-1} (\ln k)^{-1/2}$ when $k\gg 1$. This provides a quantitative measure of the correlation between earlier misfortune (represented by $k$) and eternal failure. We also show that the winner defined as the first walker overtaking the initial leader has label $k\gg 1$ with probability decaying as $\exp\!\left[-\tfrac{1}{2}(\ln k)^2\right]$.
