Abstract
We prove that in the scaling limit, the crossing probabilities of multiple interfaces in the critical planar Ising model with alternating boundary conditions are conformally invariant expressions given by the pure partition functions of multiple with . In particular, this identifies the scaling limits with ratios of specific correlation functions of conformal field theory.
Funding Statement
H.W. is supported by the Beijing Natural Science Foundation (JQ20001). E.P. is supported by the Academy of Finland grant number 340461 “Conformal invariance in planar random geometry”, by the Academy of Finland Centre of Excellence Programme grant number 346315 “Finnish centre of excellence in Randomness and STructures (FiRST)”, and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2047/1-390685813, as well as the DFG collaborative research centre “The mathematics of emerging effects” CRC-1060/211504053. During this work, E.P. was affiliated at the University of Geneva and supported by the ERC AG COMPASP, the NCCR SwissMAP, and the Swiss NSF.
Acknowledgments
We thank K. Izyurov for pointing out the useful identity (3.12) and discussing the limitations of his work. We have also enjoyed discussions with V. Beffara, N. Berestycki, A. Karrila, and K. Kytölä on this topic. We wish to thank anonymous referees for their comments, which greatly helped to improve the presentation of this article.
A part of this work was completed during E.P.’s visit at the Institut Mittag-Leffler, and during the authors’ visit to the Oberwolfach Research Institute for Mathematics (MFO), which we cordially thank for hospitality. The first version of this paper was finished during and after the workshop “Random Conformal Geometry and Related Fields” at Seoul, and we kindly thank the organizers for the inspiring meeting.
Additional address of the first author is Institute for Applied Mathematics, University of Bonn, Germany.
Citation
Eveliina Peltola. Hao Wu. "Crossing probabilities of multiple Ising interfaces." Ann. Appl. Probab. 33 (4) 3169 - 3206, August 2023. https://doi.org/10.1214/22-AAP1888
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