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Weak moment conditions for time coordinates in first-passage percolation models

Published online by Cambridge University Press:  14 July 2016

John C. Wierman
John C. Wierman*
Affiliation:
University of Minnesota
*
∗ Postal address: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, U.S.A.
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Abstract

A generalization of first-passage percolation theory proves that the fundamental convergence theorems hold provided only that the time coordinate distribution has a finite moment of a positive order. The existence of a time constant is proved by considering first-passage times between intervals of sites, rather than the usual point-to-point and point-to-line first-passage times. The basic limit theorems for the related stochastic processes follow easily by previous techniques. The time constant is evaluated as 0 when the atom at 0 of the time-coordinate distribution exceeds½.

Keywords

FIRST-PASSAGE PERCOLATIONSUBADDITIVE PROCESSGENERALIZED RENEWAL THEORYTIME CONSTANTHEIGHT PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 968 - 978
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research supported by NSF MCS 78–001168.

References

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