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On the recurrence of simple random walks on some fractals

Published online by Cambridge University Press:  14 July 2016

Zhou Xian-Yin
Zhou Xian-Yin*
Affiliation:
Beijing Normal University
*
∗Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, China. Research supported by National Natural Science Foundation of China.
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Abstract

In this paper, the recurrence or transience of simple random walks on some lattice fractals is investigated. As results, we obtain that the simple random walk on the pre-Sierpinski gasket in d dimensions is recurrent for all d ≧ 2, and on the pre-Sierpinski carpet in d dimensions it is recurrent for d = 2 and transient for all d ≧ 3.

Keywords

PRE-SIERPINSKI CARPETTRANSIENCERANDOM WALKRESISTANCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 454 - 459
Copyright
Copyright © Applied Probability Trust 1992 

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