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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.
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D. Beliaev, S. Smirnov (2009). Harmonic measure and SLE, to appear in Comm. Math. Phys
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G. Lawler (2009). Schramm-Loewner evolution, in Statistical Mechanics
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G. Lawler (2009). Multifractal analysis of the reverse flow for SLE , in Fractal Geometry and Stochastics IV
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F. Johansson Viklund, G. Lawler (2010), Optimal Hölder exponent for the SLE path, to appear in Duke Math. J
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G. Lawler and S. Sheffield (2010), The natural parametrization for the Schramm-Loewner evolution, to appear in Ann. Probab
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N.-G. Kang (2007). Boundary behavior of SLE, Journal of AMS, 20
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V. Beffara (2008). The dimension of the SLE curves, Annals of Probab. 36
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S. Smirnov (2010) Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, to appear in Ann. Math. 172
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