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The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket
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  • Published: September 1992

The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

  • Tetsuya Hattori1 &
  • Shigeo Kusuoka2 

Probability Theory and Related Fields volume 93, pages 273–284 (1992)Cite this article

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  • 19 Citations

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Summary

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is

$$\log 2/\log \left( {\frac{{7 - \sqrt 5 }}{2}} \right) = 0.79862 > 0.5 > \log 2/\log 5.$$

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References

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Author information

Authors and Affiliations

  1. Laboratory of Applied Mathematics and Mathematical Physics, Department of Information Science, Faculty of Engineering, Utsunomiya University, 321, Utsunomiya, Japan

    Tetsuya Hattori

  2. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Shigeo Kusuoka

Authors
  1. Tetsuya Hattori
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  2. Shigeo Kusuoka
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Hattori, T., Kusuoka, S. The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket. Probab. Th. Rel. Fields 93, 273–284 (1992). https://doi.org/10.1007/BF01193052

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  • Received: 15 July 1991

  • Revised: 17 February 1992

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01193052

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  • 82A99
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