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The travel time in a finite box in supercritical Bernoulli percolation


 
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1. Title Title of document The travel time in a finite box in supercritical Bernoulli percolation
 
2. Creator Author's name, affiliation, country Raphaël Cerf; Université Paris Sud; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Bernoulli percolation; travel time
 
3. Subject Subject classification 60K35;82B43
 
4. Description Abstract We consider the standard site percolation model on the three dimensional cubic lattice. Starting solely with the hypothesis that $\theta(p)>0$, we prove that, for any $\alpha>0$, there exists $\kappa>0$ such that, with probability larger than $1-1/n^\alpha$, every pair of sites inside the box $\Lambda(n)$ are joined by a path having at most $\kappa(\ln n)^2$ closed sites.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-04-12
 
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/3015
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3015
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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