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Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices
- Publication Year :
- 2020
-
Abstract
- In this article, we consider the generalised two-parameter Cauchy two-matrix model and corresponding integrable lattice equation. It is shown that with parameters chosen as $1/k_i$ when $k_i\in\mathbb{Z}_{>0}$ ($i=1,\,2$), the average characteristic polynomials admit $(k_1+k_2+2)$-term recurrence relations, which provide us spectral problems for integrable lattices. The tau function is then given by the partition function of the generalised Cauchy two-matrix model as well as Gram determinant. The simplest example with exact solvability is demonstrated.<br />Comment: 15 pages; comments are welcome
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2007.05998
- Document Type :
- Working Paper