Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 6 (2018), 1099-1237.
Almost sure multifractal spectrum of Schramm–Loewner evolution
Suppose that is a Schramm–Loewner evolution () in a smoothly bounded simply connected domain and that is a conformal map from to a connected component of for some . The multifractal spectrum of is the function which, for each , gives the Hausdorff dimension of the set of points such that as . We rigorously compute the almost sure multifractal spectrum of , confirming a prediction due to Duplantier. As corollaries, we confirm a conjecture made by Beliaev and Smirnov for the almost sure bulk integral means spectrum of , we obtain the optimal Hölder exponent for a conformal map which uniformizes the complement of an curve, and we obtain a new derivation of the almost sure Hausdorff dimension of the curve for . Our results also hold for the processes with general vectors of weight .
Duke Math. J., Volume 167, Number 6 (2018), 1099-1237.
Received: 8 March 2016
Revised: 6 October 2017
First available in Project Euclid: 28 March 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Secondary: 60G17: Sample path properties
Gwynne, Ewain; Miller, Jason; Sun, Xin. Almost sure multifractal spectrum of Schramm–Loewner evolution. Duke Math. J. 167 (2018), no. 6, 1099--1237. doi:10.1215/00127094-2017-0049. https://projecteuclid.org/euclid.dmj/1522224103