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Article Dans Une Revue Symmetry, Integrability and Geometry : Methods and Applications Année : 2023

Recursion relation for Toeplitz determinants and the discrete Painlevé II hierarchy

Résumé

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.
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Dates et versions

hal-03897674 , version 1 (14-12-2022)

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Thomas Chouteau, Sofia Tarricone. Recursion relation for Toeplitz determinants and the discrete Painlevé II hierarchy. Symmetry, Integrability and Geometry : Methods and Applications, 2023, ⟨10.3842/SIGMA.2023.030⟩. ⟨hal-03897674⟩
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