arXiv 1801.005382018-01-02nlin.SIhep-thmath-phmath.MP

The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy

Chunxia Li, Shi-Hao Li

备注：: 19 pages
DOI：: 10.1007/s00332-018-9474-x

英文摘要：

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hi- erarchy with the help of orthogonal polynomials theory and Toda-type equations. Starting from the symmetric reduction of 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 τ-function of the CKP hiearchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

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