论文标题
n随机粒子中最快的渐近学：扩展初始分布的作用和附加的漂移成分
Asymptotics for the fastest among n stochastics particles: role of an extended initial distribution and an additional drift component
论文作者
论文摘要
我们为$ n $相同的独立分布的布朗尼颗粒在吸收边界中的平均出口时间$ \barτ^{n} $得出渐近公式，以用于各种初始分布（部分均匀和指数分布）。根据初始分布的尾巴，我们在这里报告了$ \barτ^{n} $的连续代数衰减定律，该定律与经典的Weibull或Gumbell结果不同。我们在维度1和2中得出渐近公式，以进行半线和与随机模拟相比的间隔。我们还获得了布朗运动上加性常数漂移的公式。最后，我们讨论了细胞生物学中的一些应用，其中分子转导途径涉及多个步骤和长尾初始分布。
We derive asymptotic formulas for the mean exit time $\barτ^{N}$ of the fastest among $N$ identical independently distributed Brownian particles to an absorbing boundary for various initial distributions (partially uniformly and exponentially distributed). Depending on the tail of the initial distribution, we report here a continuous algebraic decay law for $\barτ^{N}$, which differs from the classical Weibull or Gumbell results. We derive asymptotic formulas in dimension 1 and 2, for half-line and an interval that we compare with stochastic simulations. We also obtain formulas for an additive constant drift on the Brownian motion. Finally, we discuss some applications in cell biology where a molecular transduction pathway involves multiple steps and a long-tail initial distribution.
