The dimension of the SLE curves

Abstract

Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa \ge 0$. We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\mathrm{Min}(2,1+\kappa /8)$.

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)

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