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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 030, 30 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.030 (Mi sigma1925) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy

Thomas Chouteaua, Sofia Tarriconeb

a Université d’Angers, CNRS, LAREMA, SFR MATHSTIC, F-49000 Angers, France
b Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France
Full-text PDF (614 kB) Citations (2)
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DOI: https://doi.org/10.3842/SIGMA.2023.030
Abstract: Solutions of the discrete Painlevé II hierarchy are shown to be in relation with a family of Toeplitz determinants describing certain quantities in multicritical random partitions models, for which the limiting behavior has been recently considered in the literature. Our proof is based on the Riemann–Hilbert approach for the orthogonal polynomials on the unit circle related to the Toeplitz determinants of interest. This technique allows us to construct a new Lax pair for the discrete Painlevé II hierarchy that is then mapped to the one introduced by Cresswell and Joshi.
Keywords: discrete Painlevé equations, orthogonal polynomials, Riemann–Hilbert problems, Toeplitz determinants.
Funding agency Grant number
Centre National de la Recherche Scientifique
IPaDEGAN 778010
Fonds De La Recherche Scientifique - FNRS O013018F
We acknowledge the support of the H2020-MSCA-RISE-2017 PROJECT No. 778010 IPaDEGAN and the International Research Project PIICQ, funded by CNRS. During the period from November 2021 to October 2022, S.T. was supported also by the Fonds de la Recherche Scientifique-FNRS under EOS project O013018F and based at the Institut de Recherche en Math´ematique et Physique of UCLouvain.
Received: December 22, 2022; in final form May 16, 2023; Published online May 28, 2023
Bibliographic databases:
Document Type: Article
MSC: 33E17, 33C47, 35Q15
Language: English
Citation: Thomas Chouteau, Sofia Tarricone, “Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy”, SIGMA, 19 (2023), 030, 30 pp.
Citation in format AMSBIB
\Bibitem{ChoTar23}
\by Thomas~Chouteau, Sofia~Tarricone
\paper Recursion Relation for Toeplitz Determinants and the Discrete Painlev\'e~II Hierarchy
\jour SIGMA
\yr 2023
\vol 19
\papernumber 030
\totalpages 30
\mathnet{http://mi.mathnet.ru/sigma1925}
\crossref{https://doi.org/10.3842/SIGMA.2023.030}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4593803}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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