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An Improved Upper Bound for the Hexagonal Lattice Site Percolation Critical Probability

Published online by Cambridge University Press:  21 November 2002

JOHN C. WIERMAN
JOHN C. WIERMAN
Affiliation:
Mathematical Sciences Department, 104 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland, MD 21218-2682, USA (e-mail: [email protected])
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Abstract

The hexagonal lattice site percolation critical probability is shown to be at most 0.79472, improving the best previous mathematically rigorous upper bound. The bound is derived by using the substitution method to compare the site model with the bond model, the latter of which is exactly solved. Shortcuts which eliminate a substantial amount of computation make the derivation of the bound possible.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 6 , November 2002 , pp. 629 - 643
Copyright
2002 Cambridge University Press

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