The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
arXiv:1801.00538 · doi:10.1007/s00332-018-9474-x
Abstract
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.
arXiv comment19 pages
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Cited by in corpus (7)
- Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
- CKP hierarchy and free Bosons
- Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
- Rank shift conditions and reductions of 2d-Toda theory
- Discrete integrable systems and condensation algorithms for Pfaffians
- Matrix integral solutions to the related Leznov lattice equations
- Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices