ON THE REGULARITY OF SLE TRACE
Copyright policy )ON THE REGULARITY OF SLE TRACE
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.
- University of California, Los Angeles United States
- Leibniz Association Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Technical University of Berlin Germany
- Weierstrass Institute Germany
ddc:510, Mathematics - Complex Variables, Probability (math.PR), article, Besov regularity, 510, Stochastic (Schramm-)Loewner evolution (SLE), Shramm-Lowner evolutions, 60J67, QA1-939, FOS: Mathematics, Complex Variables (math.CV), Mathematics, Mathematics - Probability
ddc:510, Mathematics - Complex Variables, Probability (math.PR), article, Besov regularity, 510, Stochastic (Schramm-)Loewner evolution (SLE), Shramm-Lowner evolutions, 60J67, QA1-939, FOS: Mathematics, Complex Variables (math.CV), Mathematics, Mathematics - Probability
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