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The time constant of first-passage percolation on the square lattice

Published online by Cambridge University Press:  01 July 2016

J. Theodore Cox*
Affiliation:
Syracuse University
*
Postal address: Department of Mathematics, 200 Carnegie, Syracuse University, Syracuse, NY 13210, U.S.A.

Abstract

Let μ (F) be the time constant of first-passage percolation on the square lattice with underlying distribution function F. Two theorems are presented which show, under some restrictions, that μ varies continuously in F with respect to weak convergence. These results are improvements of existing continuity theorems.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported in part by NSF Grant No. MCS76-82358.

References

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