The dimension of the SLE curves

Details The dimension of the SLE curves The dimension of the SLE curves

2002-11-20

arxiv.org/abs/math/0211322v3

Annals of Probability 2008, Vol. 36, No. 4, 1421-1452

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP364 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP364

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 $\operatorname
{Min}(2,1+\kappa/8)$.

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