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Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices
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  • Published: March 2003

Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices

  • Masato Shinoda1 

Probability Theory and Related Fields volume 125, pages 447–456 (2003)Cite this article

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Abstract.

 A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability of oriented percolation is equal to 1. In contrast it was already shown that the critical probability p c of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and ℤd lattice.

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Authors and Affiliations

  1. Department of Mathematics, Nara Women's University, Kitauoya-Nishimachi, Nara city, Nara 630-8506, Japan. e-mail: shinoda@cc.nara-wu.ac.jp, , , , , , JP

    Masato Shinoda

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  1. Masato Shinoda
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Received: 15 May 2002 / Revised version: 11 October 2002 / Published online: 21 February 2003

Mathematics Subject Classification (2000): Primary: 60K35, 82B43; Secondary: 82B26

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Cite this article

Shinoda, M. Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices. Probab Theory Relat Fields 125, 447–456 (2003). https://doi.org/10.1007/s00440-002-0247-x

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  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0247-x

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Keywords

  • Phase Transition
  • Critical Probability
  • Sierpinski Carpet
  • Percolation Problem
  • Oriented Percolation
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