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Self-avoiding process on the Sierpinski gasket
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  • Published: December 1991

Self-avoiding process on the Sierpinski gasket

  • Kumiko Hattori1 nAff2 &
  • Tetsuya Hattori2 

Probability Theory and Related Fields volume 88, pages 405–428 (1991)Cite this article

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Summary

We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study “continuum limit” processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths:

  1. (i)

    the self-avoiding process we construct in this paper;

  2. (ii)

    a deterministic motion along a “Peano curve” on the finite Sierpinski gasket;

  3. (iii)

    a deterministic motion along a line segment.

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References

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Author information

Author notes
  1. Kumiko Hattori

    Present address: Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, Komaba, 153, Tokyo, Japan

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Tsuda College, Kodaira, 187, Tokyo, Japan

    Kumiko Hattori

  2. Department of Information Science, Faculty of Engineering, Utsunomiya University, 321, Utsunomiya, Japan

    Tetsuya Hattori

Authors
  1. Kumiko Hattori
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  2. Tetsuya Hattori
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Cite this article

Hattori, K., Hattori, T. Self-avoiding process on the Sierpinski gasket. Probab. Th. Rel. Fields 88, 405–428 (1991). https://doi.org/10.1007/BF01192550

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  • Received: 08 March 1990

  • Revised: 25 September 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01192550

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Keywords

  • Stochastic Process
  • Probability Theory
  • Line Segment
  • Statistical Mechanic
  • Mathematical Biology
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