Geodesic
ON THE REGULARITY OF SLE TRACE
Forum of Mathematics, Sigma, Tome 5 (2017)

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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. 
@article{10_1017_fms_2017_18,
     author = {PETER K. FRIZ and HUY TRAN},
     title = {ON {THE} {REGULARITY} {OF} {SLE} {TRACE}},
     journal = {Forum of Mathematics, Sigma},
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     year = {2017},
     doi = {10.1017/fms.2017.18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2017.18/}
}
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PETER K. FRIZ; HUY TRAN. ON THE REGULARITY OF SLE TRACE. Forum of Mathematics, Sigma, Tome 5 (2017). doi: 10.1017/fms.2017.18

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