有向Kautz图上的随机游动

Abstract

首先给出了有向Kautz图上简单随机游动任意两点之间平均击中时间的表达式及其最大和最小值,并证明了快速收敛性.最后给出了有向Kautz图上简单随机游动从任一单点分布到稳定分布的一个最优停时规则,从而得到了最优均值.

Firstly we not only obtained the explicit formula of the expected hitting times for simple random walks on directed Kautz graphs and its maximum and minimun values,but also proved the rapid mixing of this random walk.Then we give a optimal stopping rule from any state to the stationary distribution.