Almost sure multifractal spectrum for the tip of an SLE curve. (English) Zbl 1271.82007

The chordal Schramm-Loewner evolution is a one-parameter family of probability measures on curves defined in the complex upper half-plane; and the paper deals with the behaviour at the tip of the growing SLE curve. The goal is to derive the almost sure tip multifractal spectrum for the SLE. To this end, it is shown that the latter is closely related to the multifractal spectrum of harmonic measure at the tip of the growing curve. Basically, the paper is supported by the chordal Loewner equation, and the starting point to derive the main result is the estimation of the moments of the derivative of some function using the reverse-time Loewner flow


82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
28A80 Fractals
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