Minkowski content and natural parameterization for the Schramm-Loewner evolution

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.

Published at http://dx.doi.org/10.1214/13-AOP874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Multi-point Green's functions for SLE and an estimate of Beffara
• SLE curves and natural parametrization

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