On the regularity of SLE trace

2016/11/01 by Peter K. Friz, Huy Tran, Friz, Peter K. +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.1611.01107

16 pages, 4 figures. Comments are welcome

arxiv created 2016/11/01 · arxiv updated 2016/11/04

Abstract

We revisit regularity of SLE trace, for all κ≠ 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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