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Log-gases on a quadratic lattice via discrete loop equations

By Alisa Knizel

Appears in collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

We study a general class of log-gas ensembles on a quadratic lattice. Using a variational principle we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field. Our approach is based on a q-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to a quadratic lattice. Based on joint work with Evgeni Dimitrov

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Citation data

  • DOI 10.24350/CIRM.V.19516703
  • Cite this video Knizel Alisa (4/11/19). Log-gases on a quadratic lattice via discrete loop equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19516703
  • URL https://dx.doi.org/10.24350/CIRM.V.19516703


  • Dimitrov, Evgeni; Knizel, Alisa - Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions. J. Funct. Anal. 276, No. 10, 3067-3169 (2019). - https://doi.org/10.1016/j.jfa.2018.12.008

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