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 τ-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.
CITATION STYLE
Li, C., & Li, S. H. (2019). The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy. Journal of Nonlinear Science, 29(1), 3–27. https://doi.org/10.1007/s00332-018-9474-x
Mendeley helps you to discover research relevant for your work.