论文标题
Toeplitz决定因素和离散PainlevéII层次结构的递归关系
Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
论文作者
论文摘要
离散的PainlevéII层次结构的解决方案与描述多政治随机分区模型中某些数量的toeplitz决定因素有关，在文献中最近考虑了限制行为。我们的证明是基于与感兴趣的Toeplitz决定因素有关的单位圆上的riemann-Hilbert方法。这项技术使我们能够为离散的PainlevéII层次结构构建一对新的LAX对，然后将其映射到Cresswell和Joshi引入的层次结构。
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.
