- Abstract:
-
We consider directed first-passage and last-passage percolation on the nonnegative lattice Z_+^d, d\geq2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x)=lim_{n\to\infty}n^{-1}T(\lfloor nx\rfloor) exist and are constant a.s. for x\in R_+^d, where T(z) is the passage time from the origin to the vertex z\in Z_+^d. We show that this shape function g is continuous on R_+^d, in particular at the boundaries. In two dime...
Expand abstract - Publication status:
- Published
- Publisher copy:
- 10.1214/009117904000000838
-
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- Journal:
- Annals of Probability
- Volume:
- 32
- Issue:
- 4
- Pages:
- 2908-2937
- Publication date:
- 2003-01-07
- DOI:
- ISSN:
-
0091-1798
- URN:
-
uuid:b79f5165-e63e-40c1-9607-3f293da5362c
- Source identifiers:
-
104721
- Local pid:
- pubs:104721
- Language:
- English
- Keywords:
- Copyright date:
- 2003
- Notes:
-
Published at http://dx.doi.org/10.1214/009117904000000838 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org)
Journal article
Limiting shape for directed percolation models
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