Critical Ising interfaces in multiply-connected domains

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Abstract

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.
Original languageEnglish
JournalProbability Theory and Related Fields
Volume167
Issue number1-2
Pages (from-to)379-415
Number of pages37
ISSN0178-8051
DOIs
Publication statusPublished - Feb 2017
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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