Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boutroux curves with external field: equilibrium measures without a
  minimization problem   The nonlinear steepest descent method for rank-two systems relies on the
notion of g-function. The applicability of the method ranges from orthogonal
polynomials (and generalizations) to Painleve transcendents, and integrable
wave equations (KdV, NonLinear Schroedinger, etc.).
  For the case of asymptotics of generalized orthogonal polynomials with
respect to varying complex weights we can recast the requirements for the
Cauchy-transform of the equilibrium measure into a problem of algebraic
geometry and harmonic analysis and completely solve the existence and
uniqueness issue without relying on the minimization of a functional. This
addresses and solves also the issue of the ``free boundary problem'',
determining implicitly the curves where the zeroes of the orthogonal
polynomials accumulate in the limit of large degrees and the support of the
measure. The relevance to the quasi--linear Stokes phenomenon for Painleve
equations is indicated. A numerical algorithm to find these curves in some
cases is also explained.
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34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int