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Mixed percolation on the square lattice

Published online by Cambridge University Press:  14 July 2016

John C. Wierman
John C. Wierman*
Affiliation:
The Johns Hopkins University
*
∗ Postal address: Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218, U.S.A.
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Abstract

In a planar percolation model, faces of the underlying graph, as well as the sites and bonds, may be viewed as random elements. With this viewpoint, Whitney duality allows construction of a planar dual percolation model for each planar percolation model, which applies to mixed models with sites, bonds, and faces open or closed at random. Using self-duality for percolation models on the square lattice, information is obtained about the percolative region in the mixed model.

Keywords

CRITICAL PROBABILITYPERCOLATION THEORYDUALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 247 - 259
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by the National Science Foundation under Grant No. MCS 78–01168 and MCS 81–18229.

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