The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

doi:10.1007/s00332-018-9474-x

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	The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy
	Li, Chunxia 1; Li, Shi-Hao 2,3
	2019-02-01
发表期刊	JOURNAL OF NONLINEAR SCIENCE
ISSN	0938-8974
卷号	29 期号:1 页码:3-27
摘要	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.
关键词	Matrix models Cauchy biorthogonal polynomials C-Toda lattice CKP hierarchy tau-Function theory
DOI	10.1007/s00332-018-9474-x
语种	英语
资助项目	National 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研究方向	Mathematics ; Mechanics ; Physics
WOS类目	Mathematics, Applied ; Mechanics ; Physics, Mathematical
WOS记录号	WOS:000457991200002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32510
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Shi-Hao
作者单位	1.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
推荐引用方式 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.