Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Chouteau, Thomas, Tarricone, Sofia
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211913
• 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

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...