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May 2015 Minkowski content and natural parameterization for the Schramm–Loewner evolution
Gregory F. Lawler, Mohammad A. Rezaei
Ann. Probab. 43(3): 1082-1120 (May 2015). DOI: 10.1214/13-AOP874

Abstract

We prove the existence and nontriviality of the $d$-dimensional 4 Minkowski content for the Schramm–Loewner evolution ($\mathrm{SLE} _{\kappa}$) with $\kappa<8$ and $d=1+\frac{\kappa}{8}$. We show that this is a multiple of the natural parameterization.

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Gregory F. Lawler. Mohammad A. Rezaei. "Minkowski content and natural parameterization for the Schramm–Loewner evolution." Ann. Probab. 43 (3) 1082 - 1120, May 2015. https://doi.org/10.1214/13-AOP874

Information

Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 1331.60165
MathSciNet: MR3342659
Digital Object Identifier: 10.1214/13-AOP874

Subjects:
Primary: 60J67, 60K35
Secondary: 82B27

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • May 2015
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