The Annals of Probability

The dimension of the SLE curves

Vincent Beffara

Full-text: Open access

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).

Article information

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

Dates
First available in Project Euclid: 29 July 2008

Permanent link to this document
http://projecteuclid.org/euclid.aop/1217360974

Digital Object Identifier
doi:10.1214/07-AOP364

Mathematical Reviews number (MathSciNet)
MR2435854

Zentralblatt MATH identifier
05321186

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

Keywords
SLE Hausdorff dimension

Citation

Beffara, Vincent. The dimension of the SLE curves. The Annals of Probability 36 (2008), no. 4, 1421--1452. doi:10.1214/07-AOP364. http://projecteuclid.org/euclid.aop/1217360974.


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