Abstract
We introduce a new family of first-passage percolation (FPP) models in the context of Poisson-Voronoi tesselations of ℝ d . Compared to standard FPP on ℤ d , 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).
Full Text
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call