Remarks on renewal theory for percolation processes
- 1 March 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (02) , 290-300
- https://doi.org/10.1017/s0021900200094353
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) an L 1-ergodic theorem for the unrestricted first-passage time from (0, 0) to the line X = 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
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