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First-passage percolation under weak moment conditions

Published online by Cambridge University Press:  14 July 2016

Wolfgang Reh
Wolfgang Reh*
Affiliation:
Universität Mannheim
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Abstract

Most research in first-passage percolation has been done under the assumption of a finite mean for the underlying time coordinate distribution. We demonstrate that the basic ergodic results can be derived under a weaker moment assumption, which still permits us to evaluate the time constant in the case where the atom at zero of the time coordinate distribution exceeds one-half. Further almost sure convergence is investigated more closely.

Keywords

FIRST-PASSAGE PERCOLATIONSUBADDITIVE PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 750 - 763
Copyright
Copyright © Applied Probability Trust 1979 

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