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2006 Some Properties of Annulus SLE
Dapeng Zhan
Author Affiliations +
Electron. J. Probab. 11: 1069-1093 (2006). DOI: 10.1214/EJP.v11-338

Abstract

An annulus $\mathrm{SLE}_{\kappa}$ trace tends to a single point on the target circle, and the density function of the end point satisfies some differential equation. Some martingales or local martingales are found for annulus $\mathrm{SLE}_4$, $\mathrm{SLE}_{8}$ and $\mathrm{SLE}_{8/3}$. From the local martingale for annulus $\mathrm{SLE}_4$ we find a candidate of discrete lattice model that may have annulus $\mathrm{SLE}_4$ as its scaling limit. The local martingale for annulus $\mathrm{SLE}_{8/3}$ is similar to those for chordal and radial $\mathrm{SLE}_{8/3}$. But it seems that annulus $\mathrm{SLE}_{8/3}$ does not satisfy the restriction property

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Dapeng Zhan. "Some Properties of Annulus SLE." Electron. J. Probab. 11 1069 - 1093, 2006. https://doi.org/10.1214/EJP.v11-338

Information

Accepted: 28 November 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1136.82014
MathSciNet: MR2268538
Digital Object Identifier: 10.1214/EJP.v11-338

Subjects:
Primary: 82B27
Secondary: 30C35, 60D05, 60K35, 82B43

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