Almost sure multifractal spectrum for the tip of an SLE curve

2009/11/20 by Fredrik Viklund, Fredrik Johansson Viklund, Viklund, Fredrik Johansson +2 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.0911.3983

43 pages, 2 figures

openalex publication_date 2009/11/20 · arxiv created 2011/06/12 · arxiv updated 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The tip multifractal spectrum of a two-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 one, and we give applications to the scaling of harmonic measure at the tip.

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