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Extreme paths in oriented two-dimensional percolation

Published online by Cambridge University Press:  21 June 2016

E. D. Andjel*
Affiliation:
Université d'Aix-Marseille
L. F. Gray*
Affiliation:
University of Minnesota
*
* Postal address: Université d'Aix-Marseille, 39 Rue Joliot Curie, 13453 Marseille, France. Email address: [email protected]
** Postal address: School of Mathematics, University of Minnesota, Minneapolis, MN 55455-0488, USA. Email address: [email protected]

Abstract

A useful result about leftmost and rightmost paths in two-dimensional bond percolation is proved. This result was introduced without proof in Gray (1991) in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete-time contact process and two-dimensional site percolation. Among the consequences are a natural monotonicity in the probability of percolation between different sites and a somewhat counter-intuitive correlation inequality.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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References

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