乘积图Z^2×{0,1,...,l-1}的常返性的初等证明

An Elementary Proof for the Recurrence of the Product Graph Z^2 ×{0,1,...,l-1}

我们已知二维整数格点Z^2是常返的,而三维整数格点Z^3是非常返的.本文严格证明了二维整数格点Z^2与有限线段{0,1,…1,l-1}的乘积图是常返的.证明过程只用到了概率论中的初等方法而没有用到电网络的术语.

It is well known that the two dimensional integer lattice Z^2 is recurrent,while the three dimensional integer lattice is transient.In this paper we show that the product graph Z^2×{0,1,...,ι-1}is recurrent.The proof approach only utilizes the elementary methods in probability theory(without the words of electric networks).