We study an infinite system of particles initially occupying a half-line y ⩽ 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 kth particle attains the leadership with probability e⁻² k ⁻¹(ln k)^−1/2 when k ≫ 1. This decay law provides a quantitative measure of the correlation between earlier misfortune proportional to the label k and eternal failure. We also show that the winner defined as the first walker overtaking the initial leader has label k ≫ 1 with probability decaying as .

我们研究粒子开始占据一个半线的无限系统Ÿ ⩽0和经历对整条生产线随机游动。最右边的粒子称为前导。令人惊讶的是，除原始领导者外，每个粒子都可能永远无法在整个进化过程中达到领导者的地位。对于等距初始配置中，ķ个粒子与无所获概率E中的领导^-2 ķ ^-1（LN ķ）^-1/2时ķ »1.本衰变规律提供较早不幸正比于之间的相关性的定量测量标签k和永恒的失败。我们还表明，被定义为第一个超过初始领导者的步行者的获胜者的标签k≫ 1，其概率衰减为。