Lipschitz percolation

N Dirr; P W Dondl; G R Grimmett; A E Holroyd; M Scheutzow

Lipschitz percolation

N Dirr, P W Dondl, G R Grimmett, A E Holroyd, M Scheutzow

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

27 Citations (SciVal)

Abstract

We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of 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.

Original language	English
Article number	Paper 2
Pages (from-to)	14-21
Number of pages	8
Journal	Electronic Communications in Probability
Volume	15
Publication status	Published - 2010

Cite this

@article{dc4e05b8ac364422b2276fd6fa9467d2,

title = "Lipschitz percolation",

abstract = "We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of 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.",

author = "N Dirr and Dondl, \{P W\} and Grimmett, \{G R\} and Holroyd, \{A E\} and M Scheutzow",

year = "2010",

language = "English",

volume = "15",

pages = "14--21",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Lipschitz percolation

AU - Dirr, N

AU - Dondl, P W

AU - Grimmett, G R

AU - Holroyd, A E

AU - Scheutzow, M

PY - 2010

Y1 - 2010

N2 - We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of 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.

AB - We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of 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.

UR - https://www.scopus.com/pages/publications/78649711009

M3 - Article

SN - 1083-589X

VL - 15

SP - 14

EP - 21

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - Paper 2

ER -

Lipschitz percolation

Abstract

Other files and links

Fingerprint

Cite this