Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electrostatic partners and zeros of orthogonal and multiple orthogonal
  polynomials   For a given polynomial $P$ with simple zeros, and a given semiclassical
weight $w$, we present a construction that yields a linear second-order
differential equation (ODE), and in consequence, an electrostatic model for
zeros of $P$. The coefficients of this ODE are written in terms of a dual
polynomial that we call the electrostatic partner of $P$. This construction is
absolutely general and can be carried out for any polynomial with simple zeros
and any semiclassical weight on the complex plane. An additional assumption of
quasi-orthogonality of $P$ with respect to $w$ allows us to give more precise
bounds on the degree of the electrostatic partner. In the case of orthogonal
and quasi-orthogonal polynomials, we recover some of the known results and
generalize others. Additionally, for the Hermite--Pad\'e or multiple orthogonal
polynomials of type II, this approach yields a system of linear second-order
differential equations, from which we derive an electrostatic interpretation of
their zeros in terms of a vector equilibrium. More detailed results are
obtained in the special cases of Angelesco, Nikishin, and generalized Nikishin
systems. We also discuss the discrete-to-continuous transition of these models
in the asymptotic regime, as the number of zeros tends to infinity, into the
known vector equilibrium problems. Finally, we discuss how the system of
obtained second-order ODEs yields a third-order differential equation for these
polynomials, well described in the literature. We finish the paper by
presenting several illustrative examples.

7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph