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Journal of Applied Probability Journal of Applied Probability

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Lower bounds for the critical probability in percolation models with oriented bonds

Published online by Cambridge University Press:  14 July 2016

Lawrence Gray ,
John C. Wierman  and
R. T. Smythe
Lawrence Gray
Affiliation:
University of Minnesota
John C. Wierman
Affiliation:
University of Minnesota
R. T. Smythe
Affiliation:
University of Oregon
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Abstract

In completely or partially oriented percolation models, a conceptually simple method, using barriers to enclose all open paths from the origin, improves the best previous lower bounds for the critical percolation probabilities.

Keywords

PERCOLATION CRITICAL PROBABILITY CONTACT PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 979 - 986
Copyright
Copyright © Applied Probability Trust 

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References

Bishir, J. (1963) A lower bound for the critical probability in the one-quadrant oriented-atom percolation process. J. R. Statist. Soc. B 25, 401–404.Google Scholar
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Mauldon, J. G. (1961) Asymmetric oriented percolation on a plane. Proc. 4th Berkeley Symp. Math. Statist. 2, 337–345.Google Scholar
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Smythe, R. T. and Wierman, J. C. (1978) First-Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.CrossRefGoogle Scholar

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