SLE curves and natural parametrization

Abstract

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

Published in at http://dx.doi.org/10.1214/12-AOP742 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• The Loewner equation: maps and shapes
• Multi-point Green's functions for SLE and an estimate of Beffara

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