Stochastic Loewner evolution in doubly connected domains

• 成果类型: Article
• 署名作者: Zhan, DP
• 署名单位: California Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0343-1
• 发表日期: 2004
• 页码: 340-380
• 关键词: brownian intersection exponents; conformal-invariance; plane exponents; VALUES

摘要

This paper introduces the annulus SLEkappa processes in doubly connected domains. Annulus SLE6 has the same law as stopped radial SLE6, up to a time-change. For kappa not equal 6, some weak equivalence relation exists between annulus SLEkappa and radial SLEkappa. 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 SLEkappa 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.