Almost sure multifractal spectrum for the tip of an SLE curve

Fredrik Johansson Viklund; Gregory F. Lawler

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arXiv · 0911.3983

Almost sure multifractal spectrum for the tip of an SLE curve

Fredrik Johansson Viklund·Gregory F. Lawler

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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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Fredrik Johansson Viklund, Gregory F. Lawler. 2009-11-20. Almost sure multifractal spectrum for the tip of an SLE curve. https://arxiv.org/abs/0911.3983

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