Stochastic Loewner evolution in doubly connected domains

2003/10/22 by Dapeng Zhan, Zhan, Dapeng · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.math/0310350

45 pages, no figures, published in Probability Theory and Related Fields

arxiv created 2004/09/05 · arxiv updated 2009/12/01

Abstract

This paper introduces the annulus SLE_κ processes in doubly connected domains. Annulus SLE₆ has the same law as stopped radial SLE₆, up to a time-change. For κ\not=6, some weak equivalence relation exists between annulus SLE_κ and radial SLE_κ. Annulus SLE₂ is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE₂ satisfies the reversibility property. We also consider the disc SLE_κ process defined as a limiting case of the annulus SLE's. Disc SLE₆ has the same law as stopped full plane SLE₆, up to a time-change. Disc SLE₂ is the scaling limit of loop-erased random walk, and is the reversal of radial SLE₂.

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