On the regularity of SLE trace

We revisit regularity of SLE trace, for all $κ\neq 8$, 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 $\min (1 + κ/ 8, 2)$, improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

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