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arXiv · 1611.01107

On the regularity of SLE trace

Peter K. Friz·Huy Tran
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Abstract

We revisit regularity of SLE trace, for all $\kappa \neq 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia--Rodemich--Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index $\min (1 + \kappa / 8, 2) $, improving on previous works of Werness, and also (optimal) H\"older regularity \`a la Johansson Viklund and Lawler.

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Peter K. Friz, Huy Tran. 2016-11-01. On the regularity of SLE trace. https://arxiv.org/abs/1611.01107

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