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Percolation on subsets of the square lattice

Published online by Cambridge University Press:  14 July 2016

Colin McDiarmid
Colin McDiarmid*
Affiliation:
London School of Economics and Political Science
*
∗Postal address: London School of Economics and Political Science, Houghton St., London WC 2A 2AE, U.K. Research partially supported by NRC grant A9211.
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Abstract

We adapt arguments from a paper of Seymour and Welsh concerning percolation probabilities on the infinite square lattice L to show that for certain regions R in L, if there is a positive probability of having an infinite open path in L starting at the origin then there is also a positive probability of having such a path within R.

Keywords

PERCOLATIONCRITICAL PROBABILITYSQUARE LATTICE
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 278 - 283
Copyright
Copyright © Applied Probability Trust 1980 

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References

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