Mean perimeter of the convex hull of a random walk in a semi-infinite medium.
Mean perimeter of the convex hull of a random walk in a semi-infinite medium.
复制标题
半无限介质中随机游走的凸包的平均周长。
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Majumdar
中科院分区：
文献类型：
--
作者：
M. Chupeau;O. Bénichou;S. Majumdar
我们研究了平面布朗运动的凸壳的各种性质，定义为无限反射壁存在时包围轨迹的最小凸多边形。最近(phy。Rev. E 91, 050104(R)(2015)]，我们宣布了t时刻凸壳的平均周长，用√Dt重新标度，是到墙的初始距离的非单调函数。在这篇文章中，我们首先给出了这个平均周长的推导的所有细节，特别是它的值从墙开始和靠近墙。然后，我们通过分析墙壁对凸壳的两个互补部分的影响，确定了这种令人惊讶的平均重标周长的非单调性的物理机制。最后，我们通过确定布朗运动所访问的反射壁部分的平均长度作为到壁的初始距离的函数，提供了凸壳的进一步量化。
We study various properties of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory, in the presence of an infinite reflecting wall. Recently [Phys. Rev. E 91, 050104(R) (2015)], we announced that the mean perimeter of the convex hull at time t, rescaled by √Dt, is a nonmonotonous function of the initial distance to the wall. In this article, we first give all the details of the derivation of this mean rescaled perimeter, in particular its value when starting from the wall and near the wall. We then determine the physical mechanism underlying this surprising nonmonotonicity of the mean rescaled perimeter by analyzing the impact of the wall on two complementary parts of the convex hull. Finally, we provide a further quantification of the convex hull by determining the mean length of the portion of the reflecting wall visited by the Brownian motion as a function of the initial distance to the wall.