First-passage percolation under weak moment conditions
- 1 June 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (04) , 750-763
- https://doi.org/10.1017/s0021900200033453
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
This publication has 8 references indexed in Scilit:
- On Conjectures in First Passage Percolation TheoryThe Annals of Probability, 1978
- First-passage percolation on the square lattice. IIIAdvances in Applied Probability, 1978
- Percolation Probabilities on the Square LatticePublished by Elsevier ,1978
- First-passage percolation on the square lattice, IIAdvances in Applied Probability, 1977
- First-passage percolation on the square lattice. IAdvances 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