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Random walks on dual Sierpinski gaskets

  • Interdisciplinary Physics
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Abstract

We study an unbiased random walk on dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We first determine the mean first-passage time (MFPT) between a particular pair of nodes based on the connection between the MFPTs and the effective resistance. Then, by using the Laplacian spectra, we evaluate analytically the global MFPT (GMFPT), i.e., MFPT between two nodes averaged over all node pairs. Concerning these two quantities, we obtain explicit solutions and show how they vary with the number of network nodes. Finally, we relate our results for the case of d = 2 to the well-known Hanoi Towers problem.

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Authors and Affiliations

  1. School of Computer Science, Fudan University, Shanghai, 200433, P.R. China

    Shunqi Wu & Zhongzhi Zhang

  2. Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, 200433, P.R. China

    Shunqi Wu & Zhongzhi Zhang

  3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, P.R. China

    Guanrong Chen

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  1. Shunqi Wu
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  2. Zhongzhi Zhang
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  3. Guanrong Chen
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Correspondence to Zhongzhi Zhang.

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Wu, S., Zhang, Z. & Chen, G. Random walks on dual Sierpinski gaskets. Eur. Phys. J. B 82, 91–96 (2011). https://doi.org/10.1140/epjb/e2011-20338-0

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  • DOI: https://doi.org/10.1140/epjb/e2011-20338-0

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