The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy
Li, Chunxia1; Li, Shi-Hao2,3
AbstractThis 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.
KeywordMatrix models Cauchy biorthogonal polynomials C-Toda lattice CKP hierarchy tau-Function theory
Funding ProjectNational Natural Science Foundation of China[11271266] ; National Natural Science Foundation of China[11705284] ; National Natural Science Foundation of China[11701550] ; Beijing Natural Science Foundation[1162003]
WOS Research AreaMathematics ; Mechanics ; Physics
WOS SubjectMathematics, Applied ; Mechanics ; Physics, Mathematical
WOS IDWOS:000457991200002
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Document Type期刊论文
Corresponding AuthorLi, Shi-Hao
Affiliation1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC, AMSS, POB 2719, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Dept Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Li, Chunxia,Li, Shi-Hao. The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy[J]. JOURNAL OF NONLINEAR SCIENCE,2019,29(1):3-27.
APA Li, Chunxia,&Li, Shi-Hao.(2019).The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy.JOURNAL OF NONLINEAR SCIENCE,29(1),3-27.
MLA Li, Chunxia,et al."The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy".JOURNAL OF NONLINEAR SCIENCE 29.1(2019):3-27.
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