Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The normal matrix model with a monomial potential, a vector equilibrium
  problem, and multiple orthogonal polynomials on a star   We investigate the asymptotic behavior of a family of multiple orthogonal
polynomials that is naturally linked with the normal matrix model with a
monomial potential of arbitrary degree $d+1$. The polynomials that we
investigate are multiple orthogonal with respect to a system of $d$ analytic
weights defined on a symmetric $(d+1)$-star centered at the origin. In the
first part we analyze in detail a vector equilibrium problem involving a system
of $d$ interacting measures $(\mu_{1},\ldots,\mu_{d})$ supported on star-like
sets in the plane. We show that in the subcritical regime, the first component
$\mu_{1}^{*}$ of the solution to this problem is the asymptotic zero
distribution of the multiple orthogonal polynomials. It also characterizes the
domain where the eigenvalues in the normal matrix model accumulate, in the
sense that the Schwarz function associated with the boundary of this domain can
be expressed explicitly in terms of $\mu_{1}^{*}$. The second part of the paper
is devoted to the asymptotic analysis of the multiple orthogonal polynomials.
The asymptotic results are obtained again in the subcritical regime, and they
follow from the Deift/Zhou steepest descent analysis of a Riemann-Hilbert
problem of size $(d+1)\times (d+1)$. The vector equilibrium problem and the
Riemann-Hilbert problem that we investigate are generalizations of those
studied recently by Bleher-Kuijlaars in the case $d=2$.

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat