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Limiting shape for directed percolation models

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...

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Publication status:
Published

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Publisher copy:
10.1214/009117904000000838

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
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:

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