Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble.
Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble.
复制标题
柯西二矩阵模型和 Bures 系综背后的可积格层次结构。
DOI：
10.1088/1361-6544/ac8908
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发表时间：
2022
期刊：
影响因子：
1.7
通讯作者：
Guo-Fu Yu
中科院分区：
文献类型：
--
作者：
Shi-Hao Li;Guo-Fu Yu
本文主要研究二维(2d)-Toda系统的不同约化。首先考虑对称矩矩阵和反对称矩矩阵，分别建立了对称/斜对称tau函数和二维Toda tau函数之间的微分关系。此外，受随机矩阵理论中的柯西双阵模型和Bures系综的启发，我们研究了对称情形下的秩一移位条件和斜对称情形下的秩二移位条件，由此确定了C-Toda和B-Toda族及其特殊的Lax矩阵和可积结构。
This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy. Symmetric and skew-symmetric moment matrices are first considered, resulting in differential relations between symmetric/skew-symmetric tau functions and 2d-Toda's tau functions, respectively. Furthermore, motivated by the Cauchy two-matrix model and Bures ensemble from random matrix theory, we study the rank-one shift condition in the symmetric case and rank-two shift condition in the skew-symmetric case, from which the C-Toda and B-Toda hierarchies are determined, together with their special Lax matrices and integrable structures.