Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-11-30 DOI:10.3842/SIGMA.2023.030

Thomas Chouteau, Sofia Tarricone

引用次数: 2

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.

查看原文本刊更多论文

Toeplitz行列式与离散PainlevéII族的递归关系

离散PainlevéII层次的解与描述多临界随机划分模型中某些量的Toeplitz行列式族有关，文献中最近考虑了其极限行为。我们的证明是基于单位圆上与Toeplitz行列式相关的正交多项式的Riemann-Hilbert方法。这项技术使我们能够为离散的PainlevéII层次结构构建一个新的Lax对，然后将其映射到Cresswell和Joshi引入的层次结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.