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Hausdorff Dimension of the SLE Curve Intersected with the Real Line


 
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1. Title Title of document Hausdorff Dimension of the SLE Curve Intersected with the Real Line
 
2. Creator Author's name, affiliation, country Tom Alberts; Courant Institute of Mathematical Sciences
 
2. Creator Author's name, affiliation, country Scott Sheffield; Courant Institute of Mathematical Sciences
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) SLE; Hausdorff dimension; Two-point hitting probability
 
3. Subject Subject classification 60D05;60K35;28A80
 
4. Description Abstract We establish an upper bound on the asymptotic probability of an $SLE(\kappa)$ curve hitting two small intervals on the real line as the interval width goes to zero, for the range $4 < \kappa < 8$. As a consequence we are able to prove that the random set of points in $R$ hit by the curve has Hausdorff dimension $2-8/\kappa$, almost surely.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2008-07-29
 
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/515
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-515
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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