Weak moment conditions for time coordinates in first-passage percolation models
- 1 December 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (4) , 968-978
- https://doi.org/10.2307/3213206
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
This publication has 10 references indexed in Scilit:
- First-passage percolation under weak moment conditionsJournal of Applied Probability, 1979
- On Conjectures in First Passage Percolation TheoryThe Annals of Probability, 1978
- First-passage percolation on the square lattice. IIIAdvances in Applied Probability, 1978
- First-Passage Percolation on the Square LatticeLecture Notes in Mathematics, 1978
- First-passage percolation on the square lattice. IAdvances in Applied Probability, 1977
- First-passage percolation on the square lattice, IIAdvances in Applied Probability, 1977
- Remarks on renewal theory for percolation processesJournal of Applied Probability, 1976
- Postulates for Subadditive ProcessesThe Annals of Probability, 1974
- Subadditive Ergodic TheoryThe Annals of Probability, 1973
- First-Passage PercolationJournal of the Royal Statistical Society Series B: Statistical Methodology, 1966