First-passage percolation on the square lattice, II
- 1 March 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (02) , 283-295
- https://doi.org/10.1017/s0001867800044001
Abstract
Several problems are considered in the theory of first-passage percolation on the two-dimensional integer lattice. The results include: (i) necessary and sufficient conditions for the existence of moments of first-passage times; (ii) determination of an upper bound for the time constant; (iii) an initial result concerning the maximum height of routes for first-passage times; (iv) ergodic theorems for a class of reach processes.Keywords
This publication has 2 references indexed in Scilit:
- Remarks on renewal theory for percolation processesJournal of Applied Probability, 1976
- The Probability in the Tail of a DistributionThe Annals of Mathematical Statistics, 1963