圈上的多重懒惰随机游走

MULTIPLE LAZY RANDOM WALKS ON CYCLES

本文考虑了n个定点的圈上的多重懒惰随机游走.利用偶和方法证明了其最大相遇时的期望的阶数为h_(max)×log n,其中h_(max)为圈上的一简单随机游走的最大击中时.

In this note, for the multiple lazy random walks on cycle with n vertices. By coupling method, we prove that the expectation of the maximum of meeting times is of order hmax × log n, where hmax is the maximum of hitting time for a simple random walk on cycles with n vertices.