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arXiv:1211.4146 [math.PR]AbstractReferencesReviewsResources

Minkowski content and natural parameterization for the Schramm-Loewner evolution

Gregory F. Lawler, Mohammad A. Rezaei

Published 2012-11-17, updated 2015-06-19Version 2

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.

Comments: 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)
Journal: Annals of Probability 2015, Vol. 43, No. 3, 1082-1120
Categories: math.PR
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