Euclidean models of first-passage percolation

C. Douglas Howard, Charles M. Newman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)153-170
Number of pages18
JournalProbability Theory and Related Fields
Issue number2
StatePublished - Jun 1997


  • First-passage percolation
  • Geodesic
  • Poisson process
  • Shape theorem
  • Voronoi tesselation

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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