The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy
The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy
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柯西二矩阵模型、C-Toda 格子和 CKP 层次结构
DOI：
10.1007/s00332-018-9474-x
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发表时间：
2019
影响因子：
3
通讯作者：
Li Shi-Hao
中科院分区：
文献类型：
--
作者：
Li Chunxia;Li Shi-Hao
本文主要利用正交多项式理论和Toda型方程讨论Cauchy双矩阵模型及其相应的可积族。从Cauchy双正交多项式的对称约化出发，通过引入时间流，导出了CKP型（或C-户田格）的户田方程及其Lax对.然后，将C-Toda格的矩阵积分解推广到CKP族的解，揭示了Cauchy双矩阵模型的时间依赖配分函数是CKP族的-函数.最后，从可积系统的角度建立了Cauchy双矩阵模型与Bures系综之间的联系。
This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the-function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.