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First-passage percolation on the square lattice, II

Published online by Cambridge University Press:  01 July 2016

John C. Wierman
John C. Wierman*
Affiliation:
University of Washington, Seattle
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Abstract

Several problems are considered in the theory of first-passage percolation on the two-dimensional integer lattice. The results include: (i) necessary and sufficient conditions for the existence of moments of first-passage times; (ii) determination of an upper bound for the time constant; (iii) an initial result concerning the maximum height of routes for first-passage times; (iv) ergodic theorems for a class of reach processes.

Keywords

FIRST-PASSAGE PERCOLATIONRENEWAL THEORYSUB-ADDITIVE PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 2 , June 1977 , pp. 283 - 295
Copyright
Copyright © Applied Probability Trust 1977 

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References

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