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

Keywords

FIRST-PASSAGE PERCOLATIONTIME CONSTANTSUBADDITIVE PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 864 - 879
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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