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Stochastic domination and comb percolation


 
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1. Title Title of document Stochastic domination and comb percolation
 
2. Creator Author's name, affiliation, country Alexander E Holroyd; Microsoft Research
 
2. Creator Author's name, affiliation, country James B Martin; University of Oxford
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stochastic domination, percolation, comb graph, Lipschitz embedding, first-passage percolation
 
3. Subject Subject classification 60K35; 82B43
 
4. Description Abstract There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of $\mathbb{Z}^{d-1}$ joined by a perpendicular copy) into the open set of site percolation on $\mathbb{Z}^d$, whenever the parameter p is close enough to 1 or the Lipschitz constant is sufficiently large. This is proved using several new results and techniques involving stochastic domination, in contexts that include a process of independent overlapping intervals on $\mathbb{Z}$, and first-passage percolation on general graphs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC
 
7. Date (YYYY-MM-DD) 2014-01-08
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2806
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2806
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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