Communications in Mathematical Physics

, Volume 343, Issue 1, pp 273–298 | Cite as

A Dimension Spectrum for SLE Boundary Collisions

Article
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Abstract

We consider chordal SLE\({_\kappa}\) curves for \({\kappa > 4}\), where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension \({{\rm min}\{2-8/\kappa,1\}}\). We study the random sets of points at which the curve collides with the real line at a specified “angle” and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov’s theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.

Keywords

Hausdorff Dimension Harmonic Measure Invariant Distribution Local Martingale Multifractal Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of UtahSalt Lake CityUSA
  2. 2.University of TorontoTorontoCanada
  3. 3.KTH Royal Institute of TechnologyStockholmSweden

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