Back to Search
Start Over
The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
- Publication Year :
- 2018
-
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 {\tau}-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.<br />Comment: 19 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1801.00538
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00332-018-9474-x