Remarks on renewal theory for percolation processes
- 1 June 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (2) , 290-300
- https://doi.org/10.2307/3212832
Abstract
We extend some results of Hammersley and Welsh concerning first-passage percolation on the two-dimensional integer lattice. Our results include: (i) weak renewal theorems for the unrestricted reach processes; (ii) anL1-ergodic theorem for the unrestricted first-passage time from (0, 0) to the lineX = n; and (iii) weakening of the boundedness restrictions on the underlying distribution in Hammersley and Welsh's weak renewal theorems for the cylinder reach processes.Keywords
This publication has 2 references indexed in Scilit:
- The Ergodic Theory of Subadditive Stochastic ProcessesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1968
- First-Passage PercolationJournal of the Royal Statistical Society Series B: Statistical Methodology, 1966