Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level Spacing Distribution of Critical Random Matrix Ensembles   We consider unitary invariant random matrix ensembles which obey spectral
statistics different from the Wigner-Dyson, including unitary ensembles with
slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas
model. If the deformation parameters in these matrix ensembles are small, the
asymptotically translational-invariant region in the spectral bulk is
universally governed by a one-parameter generalization of the sine kernel. We
provide an analytic expression for the distribution of the eigenvalue spacings
of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and
the Poisson distributions, by determining the Fredholm determinant of the
universal kernel in terms of a Painleve VI transcendental function.

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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci