Abstract
We introduce a new family of first-passage percolation (FPP) models in the context of Poisson-Voronoi tesselations of ℝd. Compared to standard FPP on ℤd, these models have some technical complications but also have the advantage of statistical isotropy. We prove two almost sure results: a shape theorem (where isotropy implies an exact Euclidean ball for the asymptotic shape) and nonexistence of certain doubly infinite geodesics (where isotropy yields a stronger result than in standard FPP).
Original language | English (US) |
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Pages (from-to) | 153-170 |
Number of pages | 18 |
Journal | Probability Theory and Related Fields |
Volume | 108 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1997 |
Keywords
- First-passage percolation
- Geodesic
- Poisson process
- Shape theorem
- Voronoi tesselation
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty