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AB percolation on bond-decorated graphs

Published online by Cambridge University Press:  14 July 2016

Martin J. B. Appel
Affiliation:
University of Iowa
John C. Wierman
Affiliation:
The Johns Hopkins University

Abstract

It is known [8] that a certain class of bond-decorated graphs exhibits multiple AB percolation phase transitions. Sufficient conditions are given under which the corresponding AB percolation critical probabilities may be identified as points of intersection of the graph of a certain polynomial with the boundary of the percolative region of an associated two-parameter bond-site percolation model on the underlying undecorated graph. The main result of the article is used to prove that the graphs in [8] exhibit multiple AB percolation critical probabilities. The possibility of identifying AB percolation critical exponents with corresponding limits for the bond-site model is discussed.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1993 

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References

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