Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tracy-Widom GUE law and symplectic invariants   We establish the relation between two objects: an integrable system related
to Painleve II equation, and the symplectic invariants of a certain plane curve
\Sigma_{TW} describing the average eigenvalue density of a random hermitian
matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This
explains directly how the Tracy-Widow law F_{GUE}, governing the distribution
of the maximal eigenvalue in hermitian random matrices, can also be recovered
from symplectic invariants.

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: physics