The Annals of Probability

Hausdorff dimensions for SLE6

Vincent Beffara

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Abstract

We prove that the Hausdorff dimension of the trace of SLE6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler–Schramm–Werner) that the dimension of its boundary is 4/3. We also prove that, for all κ<8, the SLEκ trace has cut-points.

Article information

Source
Ann. Probab. Volume 32, Number 3B (2004), 2606-2629.

Dates
First available in Project Euclid: 6 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.aop/1091813625

Digital Object Identifier
doi:10.1214/009117904000000072

Mathematical Reviews number (MathSciNet)
MR2078552

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. Hausdorff dimensions for SLE 6 . Ann. Probab. 32 (2004), no. 3B, 2606--2629. doi:10.1214/009117904000000072. http://projecteuclid.org/euclid.aop/1091813625.


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