The dimension of the SLE curves

Vincent Beffara

doi:10.1214/07-AOP364

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Home > Journals > Ann. Probab. > Volume 36 > Issue 4 > Article

July 2008 The dimension of the SLE curves

Vincent Beffara

Ann. Probab. 36(4): 1421-1452 (July 2008). DOI: 10.1214/07-AOP364

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Abstract

Let γ be the curve generating a Schramm–Loewner Evolution (SLE) process, with parameter κ≥0. We prove that, with probability one, the Hausdorff dimension of γ is equal to Min(2, 1+κ/8).