Critical Ising interfaces in multiply-connected domains

• 成果类型: Article
• 署名作者: Izyurov, Konstantin
• 署名单位: University of Helsinki
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0685-x
• 发表日期: 2017
• 页码: 379-415
• 关键词: erased random-walks; conformal-invariance; SCALING LIMITS

摘要

We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and we also treat the radial SLE case. In the case of simply and doubly connected domains, the limiting processes are described explicitly in terms of rational and elliptic functions, respectively.