ZHU Lin, YAO Qiang, . An Elementary Proof for the Recurrence of the Product Graph \mathbb{Z}^2\times\{0,1,\ldots,l-1\}[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(3): 275-283.
Citation:
ZHU Lin, YAO Qiang, . An Elementary Proof for the Recurrence of the Product Graph \mathbb{Z}^2\times\{0,1,\ldots,l-1\}[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(3): 275-283.
ZHU Lin, YAO Qiang, . An Elementary Proof for the Recurrence of the Product Graph \mathbb{Z}^2\times\{0,1,\ldots,l-1\}[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(3): 275-283.
Citation:
ZHU Lin, YAO Qiang, . An Elementary Proof for the Recurrence of the Product Graph \mathbb{Z}^2\times\{0,1,\ldots,l-1\}[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(3): 275-283.
An Elementary Proof for the Recurrence of the Product Graph \mathbbZ^2\times\0,1,\ldots,l-1\
It is well known that the two dimensional integer lattice \mathbbZ^2 is recurrent, while the three dimensional integer lattice is transient. In this paper we show that the product graph \mathbbZ^2\times\0,1,\ldots,l-1\ is recurrent. The proof approach only utilizes the elementary methods in probability theory (without the words of electric networks).
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