| �˻�ͼ\mathbb{Z}^2\times\{0,1,\ldots,l-1\}�ij����Եij���֤�� |
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| 引用本文： | ����,Ҧǿ.�˻�ͼ\mathbb{Z}^2\times\{0,1,\ldots,l-1\}�ij����Եij���֤��[J].应用概率统计,2018,34(3):275-283. |
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| 作者姓名： | ���� Ҧǿ |
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| 作者单位： | ?й??????????????????о??, ????, 100872; ???????????????, ???, 200241 |
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| 摘 要： |
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| 关 键 词： | ????ζ? ???? ?????? |
An Elementary Proof for the Recurrence of the Product Graph \mathbb{Z}^2\times\{0,1,\ldots,l-1\} |
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| 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 Statisties,2018,34(3):275-283. |
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| Authors: | ZHU Lin YAO Qiang |
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| Institution: | Institute of Statistics and Big Data, Renmin University of China, Beijing, 100872, China; School of Statistics, East China Normal University,Shanghai, 200241, China |
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| Abstract: | It is well known that the two dimensional integer lattice \mathbb{Z}^2 is recurrent, while the three dimensional integer lattice is transient. In this paper we show that the product graph \mathbb{Z}^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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| Keywords: | random walk product graph recurrence |
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