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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 41 open journal systems 


Some Properties of Annulus SLE

Dapeng Zhan, U. C. Berkeley


Abstract
An annulus SLEκ 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 SLE4, SLE8 and SLE8/3. From the local martingale for annulus SLE4 we find a candidate of discrete lattice model that may have annulus SLE4 as its scaling limit. The local martingale for annulus SLE8/3 is similar to those for chordal and radial SLE8/3. But it seems that annulus SLE8/3 does not satisfy the restriction property


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Pages: 1069-1093

Published on: November 28, 2006
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Electronic Journal of Probability. ISSN: 1083-6489