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 Electronic Communications in Probability > Vol. 15(2010) > Paper 2 open journal systems 


Lipschitz percolation

Nicolas Dirr, University of Bath
Patrick W. Dondl, University of Bonn
Geoffrey R. Grimmett, Cambridge University
Alexander E. Holroyd, Microsoft Research; University of British Columbia
Michael Scheutzow, Technical University, Berlin


Abstract
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.


Full text: PDF

Pages: 14-21

Published on: January 21, 2010


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Electronic Communications in Probability. ISSN: 1083-589X