Lipschitz Percolation

  • Nicolas Dirr ,
  • Patrick Dondl ,
  • Geoffrey Grimmett ,
  • Alexander Holroyd ,
  • Michael Scheutzow

Electronic Communications in Probability | , Vol 15: pp. 14-21

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We prove the existence of a (random) Lipschitz function F : Zd−1 → Z+ such that, for every x ∈ Zd−1, the site (x, F(x)) is open in a site percolation process on Zd . The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1. Alexander Holroyd