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Harmonic Measure and SLE

Beliaev, Dmitry
Published in Communications in Mathematical Physics. 2009, vol. 290, no. 2, p. 577 - 595
Abstract In this paper we study the multifractal structure of Schramm's SLE curves. We derive the values of the (average) spectrum of harmonic measure and prove Duplantier's prediction for the multifractal spectrum of SLE curves. The spectrum can also be used to derive estimates of the dimension, Hölder exponent and other geometrical quantities. The SLE curves provide perhaps the only example of sets where the spectrum is non-trivial yet exactly computable.
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BELIAEV, Dmitry, SMIRNOV, Stanislav. Harmonic Measure and SLE. In: Communications in Mathematical Physics, 2009, vol. 290, n° 2, p. 577 - 595. https://archive-ouverte.unige.ch/unige:8523

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Deposited on : 2010-07-02

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