Hausdorff dimensions for SLE_6

Details Hausdorff dimensions for SLE_6 Hausdorff dimensions for SLE_6

2002-04-16

arxiv.org/abs/math/0204208v3

Annals of Probability 2004, Vol. 32, No. 3, 2606-2629

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000072 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000072

We prove that the Hausdorff dimension of the trace of SLE_6 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 \kappa<8, the SLE_{\kappa} trace has cut-points.

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