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Geometry of the random interlacement


 
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1. Title Title of document Geometry of the random interlacement
 
2. Creator Author's name, affiliation, country Eviatar Ben Procaccia; Weizmann Institute of science
 
2. Creator Author's name, affiliation, country Johan Tykesson; Weizmann Institute of science
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Interlacements; Stochastic dimension
 
3. Subject Subject classification Probability
 
4. Description Abstract We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in [1] to prove the following: Given that two vertices $x,y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $\lceil d/2 \rceil$ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $\lceil d/2 \rceil-1$ trajectories.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swedish Research Council, Israeli Science foundation
 
7. Date (YYYY-MM-DD) 2011-09-26
 
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/1660
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1660
 
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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