The Annals of Probability

SLE curves and natural parametrization

Gregory F. Lawler and Wang Zhou

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Abstract

Developing the theory of two-sided radial and chordal $\mathit{SLE}$, we prove that the natural parametrization on $\mathit{SLE}_{\kappa}$ curves is well defined for all $\kappa<8$. Our proof uses a two-interior-point local martingale.

Article information

Source
Ann. Probab., Volume 41, Number 3A (2013), 1556-1584.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1367241506

Digital Object Identifier
doi:10.1214/12-AOP742

Mathematical Reviews number (MathSciNet)
MR3098684

Zentralblatt MATH identifier
1288.60098

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60J60: Diffusion processes [See also 58J65] 30C20: Conformal mappings of special domains 28A80: Fractals [See also 37Fxx]

Keywords
SLE natural parametrization Doob–Meyer decomposition local martingale

Citation

Lawler, Gregory F.; Zhou, Wang. SLE curves and natural parametrization. Ann. Probab. 41 (2013), no. 3A, 1556--1584. doi:10.1214/12-AOP742. https://projecteuclid.org/euclid.aop/1367241506


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References

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