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