On the time constant of high dimensional first passage percolation

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2 Scopus citations


We study the time constant µ(e1) in first passage percolation on ℤd as a function of the dimension. We prove that if the passage times have finite mean, (equation found) where a ∈ [0,∞] is a constant that depends only on the behavior of the distribution of the passage times at 0. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a d-dimensional cube or diamond, provided that d is large enough.

Original languageEnglish (US)
JournalElectronic Journal of Probability
StatePublished - 2016


  • Eden model
  • First passage percolation
  • Limit shape
  • Time constant

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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