Lipschitz percolation

2009/11/17 by N. Dirr, P. W. Dondl, Dirr, N. +7 · 1 citation
Mathematics · #60K35 #82B20 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35 #msc:82B20

paper · pdf · doi:10.48550/arxiv.0911.3384

Minor error corrected, and reference updated

arxiv created 2009/11/25 · arxiv updated 2009/12/08

Abstract

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

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