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The dimension of the SLE curves

Vincent Beffara
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Abstract

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

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Vincent Beffara. 2008-08-27. The dimension of the SLE curves. https://doi.org/10.1214/07-aop364

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