Annals of Probability

The dimension of the SLE curves

Vincent Beffara

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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).

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Ann. Probab., Volume 36, Number 4 (2008), 1421-1452.

First available in Project Euclid: 29 July 2008

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Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G17: Sample path properties 28A80: Fractals [See also 37Fxx]

SLE Hausdorff dimension


Beffara, Vincent. The dimension of the SLE curves. Ann. Probab. 36 (2008), no. 4, 1421--1452. doi:10.1214/07-AOP364.

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