Some Properties of Annulus SLE

2006/07/27 by Dapeng Zhan, Zhan, Dapeng
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.math/0607720

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

arxiv created 2006/07/27 · openalex publication_date 2006/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An annulus SLE_κ 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 SLE_8/3. 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 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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