Note on the existence and modulus of continuity of the $${\textit{SLE}}_8$$ SLE 8 curve

Marcelo Alvisio () and Gregory Lawler ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 1, 5-22

Abstract: We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for $$\kappa =8$$ κ = 8 . The main idea in the proof of these estimates is applying the Girsanov theorem to reduce the problem to estimates about one-dimensional Brownian motion. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Schramm–Loewner evolution; Modulus of continuity (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00184-013-0471-7

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