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First-passage percolation on the square lattice. III

Published online by Cambridge University Press:  01 July 2016

R. T. Smythe and
John C. Wierman
R. T. Smythe
Affiliation:
University of Oregon
John C. Wierman
Affiliation:
University of Minnesota
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Abstract

The principal results of this paper concern the asymptotic behavior of the number of arcs in the optimal routes of first-passage percolation processes on the square lattice. Assuming that the underlying distribution has an atom at zero less than λ–1, where λ is the connectivity constant, Lp and (in some cases) almost sure convergence theorems are proved for the normalized route length processes. The proofs involve the extension of much of the existing theory of first-passage percolation to the case where negative time coordinates are permitted.

Keywords

FIRST-PASSAGE PERCOLATIONROUTE LENGTHSUBADDITIVE PROCESSES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 1 , March 1978, pp. 155 - 171
Copyright
Copyright © Applied Probability Trust 1978 

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Footnotes

∗

Research partially supported at the University of Washington by NSF Grant MCS 76–07279.

References

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