ON THE REGULARITY OF SLE TRACE

Abstract

We revisit regularity of SLE trace, for all $\unicode[STIX]{x1D705}\neq 8$ , 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 $\min (1+\unicode[STIX]{x1D705}/8,2)$ , improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

Keywords

• 60J67