## Electronic Journal of Probability

### Some Properties of Annulus SLE

Dapeng Zhan

#### 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

#### Article information

Source
Electron. J. Probab., Volume 11 (2006), paper no. 41, 1069-1093.

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

https://projecteuclid.org/euclid.ejp/1464730576

Digital Object Identifier
doi:10.1214/EJP.v11-338

Mathematical Reviews number (MathSciNet)
MR2268538

Zentralblatt MATH identifier
1136.82014

Rights

#### Citation

Zhan, Dapeng. Some Properties of Annulus SLE. Electron. J. Probab. 11 (2006), paper no. 41, 1069--1093. doi:10.1214/EJP.v11-338. https://projecteuclid.org/euclid.ejp/1464730576

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