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Critical Ising interfaces in multiply-connected domains

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.

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Acknowledgments

The author is grateful to the referee for valuable remarks. Work supported by Academy of Finland.

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Correspondence to Konstantin Izyurov.

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Izyurov, K. Critical Ising interfaces in multiply-connected domains. Probab. Theory Relat. Fields 167, 379–415 (2017). https://doi.org/10.1007/s00440-015-0685-x

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  • DOI: https://doi.org/10.1007/s00440-015-0685-x

Mathematics Subject Classification

  • 82B20
  • 60J67