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Euclidean models of first-passage percolation
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  • Published: June 1997

Euclidean models of first-passage percolation

  • C. Douglas Howard1 &
  • Charles M. Newman2 

Probability Theory and Related Fields volume 108, pages 153–170 (1997)Cite this article

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  • 52 Citations

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Summary.

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).

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Authors and Affiliations

  1. Polytechnic University, 6 Metrotech Center, Brooklyn, NY 11201, USA (e-mail: howard@math.poly.edu), , , , , , US

    C. Douglas Howard

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (e-mail: newman@cims.nyu.edu), , , , , , US

    Charles M. Newman

Authors
  1. C. Douglas Howard
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  2. Charles M. Newman
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Additional information

Received: 21 May 1996 / In revised form: 19 November 1996

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Howard, C., Newman, C. Euclidean models of first-passage percolation. Probab Theory Relat Fields 108, 153–170 (1997). https://doi.org/10.1007/s004400050105

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  • Issue Date: June 1997

  • DOI: https://doi.org/10.1007/s004400050105

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  • Key words and phrases: First-passage percolation
  • Poisson process
  • Voronoi tesselation
  • shape theorem
  • geodesic
  • Mathematics Subject Classification (1991): Primary 60K35
  • 60G55; secondary 82D30.
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