Hausdorff dimensions for SLE6

Vincent Beffara

doi:10.1214/009117904000000072

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Home > Journals > Ann. Probab. > Volume 32 > Issue 3B > Article

July 2004 Hausdorff dimensions for SLE₆

Vincent Beffara

Ann. Probab. 32(3B): 2606-2629 (July 2004). DOI: 10.1214/009117904000000072

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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 SLE_κ trace has cut-points.