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Large Deviations for the Two-Dimensional Two-Component Plasma

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Abstract

We derive a large deviations principle for the two-dimensional two-component plasma in a box. As a consequence, we obtain a variational representation for the free energy, and also show that the macroscopic empirical measure of either positive or negative charges converges to the uniform measure. An appendix, written by Wei Wu, discusses applications to the subcritical complex Gaussian multiplicative chaos.

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Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ. Paris 06, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, 75005, Paris, France

    Thomas Leblé & Sylvia Serfaty

  2. Institut Universitaire de France, Paris, France

    Sylvia Serfaty

  3. Courant Institute, New York University, 251 Mercer st, New York, NY, 10012, USA

    Sylvia Serfaty & Ofer Zeitouni

  4. Department of Mathematics, Weizmann Institute of Science, POB 26, Rehovot, 76100, Israel

    Ofer Zeitouni

Authors
  1. Thomas Leblé
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  2. Sylvia Serfaty
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  3. Ofer Zeitouni
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Corresponding author

Correspondence to Sylvia Serfaty.

Additional information

Communicated by A. Borodin

With an appendix by Wei Wu. Courant Institute, New York University, 251 Mercer st, New York, NY 10012, USA & New York University-Shanghai, 1555 Century Ave, Pudong Shanghai, CN 200122, China. weiwu@cims.nyu.edu

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Leblé, T., Serfaty, S. & Zeitouni, O. Large Deviations for the Two-Dimensional Two-Component Plasma. Commun. Math. Phys. 350, 301–360 (2017). https://doi.org/10.1007/s00220-016-2735-3

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  • DOI: https://doi.org/10.1007/s00220-016-2735-3

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