Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
Solutions of the discrete Painlevé II hierarchy are shown to be in relation to a family of Toeplitz determinants describing certain quantities in multicritical random partition models, for which the limiting behavior has been recently considered in the literature. Our proof is based on the Riemann-H...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211913 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy. Thomas Chouteau and Sofia Tarricone. SIGMA 19 (2023), 030, 30 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862681266988515328 |
|---|---|
| author | Chouteau, Thomas Tarricone, Sofia |
| author_facet | Chouteau, Thomas Tarricone, Sofia |
| citation_txt | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy. Thomas Chouteau and Sofia Tarricone. SIGMA 19 (2023), 030, 30 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Solutions of the discrete Painlevé II hierarchy are shown to be in relation to a family of Toeplitz determinants describing certain quantities in multicritical random partition 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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| first_indexed | 2026-03-17T00:46:36Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211913 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T00:46:36Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chouteau, Thomas Tarricone, Sofia 2026-01-16T11:18:15Z 2023 Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy. Thomas Chouteau and Sofia Tarricone. SIGMA 19 (2023), 030, 30 pages 1815-0659 2020 Mathematics Subject Classification: 33E17; 33C47; 35Q15 arXiv:2211.16898 https://nasplib.isofts.kiev.ua/handle/123456789/211913 https://doi.org/10.3842/SIGMA.2023.030 Solutions of the discrete Painlevé II hierarchy are shown to be in relation to a family of Toeplitz determinants describing certain quantities in multicritical random partition 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. 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 also supported by the Fonds de la Recherche Scientifique-FNRS under the EOS project O013018F and based at the Institut de Recherche en Mathématique et Physique of UCLouvain. The authors are grateful to Mattia Cafasso for the inspiration given to work on this project and his guidance. The authors also want to thank the referees of this paper for their useful comments and suggestions. S.T. is also grateful to Giulio Ruzza for meaningful conversations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy Article published earlier |
| spellingShingle | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy Chouteau, Thomas Tarricone, Sofia |
| title | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy |
| title_full | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy |
| title_fullStr | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy |
| title_full_unstemmed | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy |
| title_short | Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy |
| title_sort | recursion relation for toeplitz determinants and the discrete painlevé ii hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211913 |
| work_keys_str_mv | AT chouteauthomas recursionrelationfortoeplitzdeterminantsandthediscretepainleveiihierarchy AT tarriconesofia recursionrelationfortoeplitzdeterminantsandthediscretepainleveiihierarchy |