Euclidean models of first-passage percolation
- Cite this article as:
- Howard, C. & Newman, C. Probab Theory Relat Fields (1997) 108: 153. doi:10.1007/s004400050105
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).