Some Properties of Annulus SLE

Details Some Properties of Annulus SLE Some Properties of Annulus SLE

2006-07-27

arxiv.org/abs/math/0607720v1

Mathematics

Probability

29 pages, no figures, submitted to the Electronic Journal of Probability

Scientific paper

An annulus 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 SLE$_4$, SLE$_8$ and SLE$_{8/3}$. From the local martingale for annulus SLE$_4$ we find a candidate of discrete lattice model that may have annulus SLE$_4$ as its scaling limit. The local martingale for annulus SLE$_{8/3}$ is similar to those for chordal and radial SLE$_{8/3}$. But it seems that annulus SLE$_{8/3}$ does not satisfy the restriction property.

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