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Construction of a short path in high-dimensional first passage percolation


 
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1. Title Title of document Construction of a short path in high-dimensional first passage percolation
 
2. Creator Author's name, affiliation, country Olivier Couronné; Universite Paris-Ouest
 
2. Creator Author's name, affiliation, country Nathanaël Enriquez; Universite Paris-Ouest
 
2. Creator Author's name, affiliation, country Lucas Gerin; Universite Paris-Ouest
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) first passage percolation; time constant; limit shape
 
3. Subject Subject classification 60K35;82B43
 
4. Description Abstract For first passage percolation in $\mathbb{Z}^d$ with large $d$, we construct a path connecting the origin to $\{x_1 =1\}$, whose passage time has optimal order $\log d/d$. Besides, an improved lower bound for the "diagonal" speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidean ball in dimension larger than 35.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR MEMEMO
 
7. Date (YYYY-MM-DD) 2011-01-09
 
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/1595
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1595
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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