Almost sure multifractal spectrum for the tip of an SLE curve

Fredrik Johansson Viklund Department of Mathematics, Columbia University Gregory F. Lawler Department of Mathematics and Department of Statistics, University of Chicago

Probability Spectral Theory and Operator Algebra mathscidoc:1701.28001

Acta Mathematica, 209, (2), 265-322, 2010.11
The tip multifractal spectrum of a 2-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm–Loewner evolution (SLE) curve, we prove that the spectrum is valid with probability 1, and we give applications to the scaling of harmonic measure at the tip.
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@inproceedings{fredrik2010almost,
  title={Almost sure multifractal spectrum for the tip of an SLE curve},
  author={Fredrik Johansson Viklund, and Gregory F. Lawler},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203359821130763},
  booktitle={Acta Mathematica},
  volume={209},
  number={2},
  pages={265-322},
  year={2010},
}
Fredrik Johansson Viklund, and Gregory F. Lawler. Almost sure multifractal spectrum for the tip of an SLE curve. 2010. Vol. 209. In Acta Mathematica. pp.265-322. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203359821130763.
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