The Annals of Probability

Minkowski content and natural parameterization for the Schramm–Loewner evolution

Gregory F. Lawler and Mohammad A. Rezaei

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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.

Article information

Source
Ann. Probab., Volume 43, Number 3 (2015), 1082-1120.

Dates
First available in Project Euclid: 5 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1430830278

Digital Object Identifier
doi:10.1214/13-AOP874

Mathematical Reviews number (MathSciNet)
MR3342659

Zentralblatt MATH identifier
1331.60165

Subjects
Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B27: Critical phenomena

Keywords
Schramm–Loewner evolution Minkowski content natural parameterization

Citation

Lawler, Gregory F.; Rezaei, Mohammad A. Minkowski content and natural parameterization for the Schramm–Loewner evolution. Ann. Probab. 43 (2015), no. 3, 1082--1120. doi:10.1214/13-AOP874. https://projecteuclid.org/euclid.aop/1430830278


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References

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