PR ] 1 7 N ov 2 00 3 Limiting Shape for Directed Percolation Models

@inproceedings{Martin2004PR1,
  title={PR ] 1 7 N ov 2 00 3 Limiting Shape for Directed Percolation Models},
  author={James B. Martin},
  year={2004}
}
We consider directed first-passage and last-passage percolation on the non-negative lattice Zd+, d ≥ 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = limn→∞ n T (⌊nx⌋) exist and are constant a.s. for x ∈ Rd+, where T (z) is the passage time from the origin to the vertex z… CONTINUE READING