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Lipschitz percolation


 
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1. Title Title of document Lipschitz percolation
 
2. Creator Author's name, affiliation, country Nicolas Dirr; University of Bath
 
2. Creator Author's name, affiliation, country Patrick W. Dondl; University of Bonn
 
2. Creator Author's name, affiliation, country Geoffrey R. Grimmett; Cambridge University
 
2. Creator Author's name, affiliation, country Alexander E. Holroyd; Microsoft Research; University of British Columbia
 
2. Creator Author's name, affiliation, country Michael Scheutzow; Technical University, Berlin
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) percolation, Lipschitz embedding, random surface
 
3. Subject Subject classification 60K35, 82B20
 
4. Description Abstract We prove the existence of a (random) Lipschitz function $F:\mathbb{Z}^{d-1}\to\mathbb{Z}^+$ such that, for every $x\in\mathbb{Z}^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\mathbb{Z}^{d}$. The Lipschitz constant may be taken to be $1$ when the parameter $p$ of the percolation model is sufficiently close to $1$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Microsoft Research; Deutsche Forschungsgemeinschaft
 
7. Date (YYYY-MM-DD) 2010-01-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1521
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1521
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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