Almost sure multifractal spectrum for the tip of an SLE curve

Details Almost sure multifractal spectrum for the tip of an SLE curve Almost sure multifractal spectrum for the tip of an SLE curve

2009-11-20

arxiv.org/abs/0911.3983v2

Mathematics

Probability

43 pages, 2 figures

Scientific paper

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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