Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling Limits of Planar Symplectic Ensembles   We consider various asymptotic scaling limits $N\to\infty$ for the $2N$
complex eigenvalues of non-Hermitian random matrices in the symmetry class of
the symplectic Ginibre ensemble. These are known to be integrable, forming
Pfaffian point processes, and we obtain limiting expressions for the
corresponding kernel for different potentials. The first part is devoted to the
symplectic Ginibre ensemble with the Gaussian potential. We obtain the
asymptotic at the edge of the spectrum in the vicinity of the real line. The
unifying form of the kernel allows us to make contact with the bulk scaling
along the real line and with the edge scaling away from the real line, where we
recover the known determinantal process of the complex Ginibre ensemble. Part
two covers ensembles of Mittag-Leffler type with a singularity at the origin.
For potentials $Q(\zeta)=|\zeta|^{2\lambda}-(2c/N)\log|\zeta|$, with
$\lambda>0$ and $c>-1$, the limiting kernel obeys a linear differential
equation of fractional order $1/\lambda$ at the origin. For integer
$m=1/\lambda$ it can be solved in terms of Mittag-Leffler functions. In the
last part, we derive Ward's equation for planar symplectic ensembles for a
general class of potentials. It serves as a tool to investigate the Gaussian
and singular Mittag-Leffler universality class. This allows us to determine the
functional form of all possible limiting kernels (if they exist) that are
translation invariant, up to their integration domain.

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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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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: nlin
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The categories of this paper are: chem-ph