Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-parameter generalisations of Cauchy bi-orthogonal polynomials and
  integrable lattices   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.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph