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Upper bound on the expected size of the intrinsic ball


 
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1. Title Title of document Upper bound on the expected size of the intrinsic ball
 
2. Creator Author's name, affiliation, country Artem Sapozhnikov; EURANDOM
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Critical percolation; high-dimensional percolation; triangle condition; chemical distance; intrinsic ball
 
3. Subject Subject classification 60K35; 82B43
 
4. Description Abstract We give a short proof of Theorem 1.2 (i) from the paper "The Alexander-Orbach conjecture holds in high dimensions" by G. Kozma and A. Nachmias. We show that the expected size of the intrinsic ball of radius $r$ is at most $Cr$ if the susceptibility exponent is at most 1. In particular, this result follows if the so-called triangle condition holds.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-07-23
 
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/1553
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1553
 
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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