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arXiv:math/0211322 [math.PR]AbstractReferencesReviewsResources

The dimension of the SLE curves

Vincent Beffara

Published 2002-11-20, updated 2008-08-27Version 3

Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa\geq0$. We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\operatorname {Min}(2,1+\kappa/8)$.

Comments: Published in at http://dx.doi.org/10.1214/07-AOP364 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2008, Vol. 36, No. 4, 1421-1452
Categories: math.PR, math.CV
Subjects: 60D05, 60G17, 28A80
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