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On the continuity of the time constant of first-passage percolation

Published online by Cambridge University Press:  14 July 2016

J. Theodore Cox  and
Harry Kesten
J. Theodore Cox*
Affiliation:
Syracuse University
Harry Kesten*
Affiliation:
Cornell University
*
∗Postal address: Department of Mathematics, Syracuse University, 200 Carnegie, Syracuse, NY 13210, U.S.A.
∗∗Postal address: Department of Mathematics, White Hall, Cornell University, Ithaca, NY 14850, U.S.A.
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Abstract

Let U be the distribution function of the non-negative passage time of an individual edge of the square lattice, and let a0n be the minimal passage time from (0, 0) to (n, 0). The process a0n/n converges in probability as n → ∞to a finite constant μ (U) called the time constant. It is proven that μ (Uk)→ μ(U) whenever Uk converges weakly to U.

Keywords

FIRST-PASSAGE PERCOLATIONTIME CONSTANT
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 809 - 819
Copyright
Copyright © Applied Probability Trust 1981 

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References

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