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This paper deals with products and ratios of average characteristic polynomials for unitary ensembles.
An isomonodromy approach to the theory of two-dimensional quantum gravity
A. R. Its, A. V. Kitaev, and A. S. Fokas · 1990
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Intersection theory on the moduli space of curves and the matrix Airy function
Maxim Kontsevich · 1992
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Correlators of spectral determinants in quantum chaos
A. V. Andreev and B. D. Simons · 1995
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A. Mironov S. Kharchev, A. Marshakov and A. Morozov · 1995
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Unitary matrix integrals in the framework of the generalized Kontsevich model
A. Morozov A. Mironov and G. W. Semenoff · 1996
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M. Adler, T. Shiota, and P. van Moerbeke · 1998
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou · 1999
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Characteristic polynomials of random matrices
E. Brézin and S. Hikami · 2000
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Characteristic polynomials of random matrices at edge singularities
E. Brézin and S. Hikami · 2000
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Random matrix theory and ζ ( 1 / 2 + i t ) \zeta(1/2+it)
J. P. Keating and N. C. Snaith · 2000
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Generating functions for intersection numbers on moduli spaces of curves
A. Okounkov · 2002
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Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
G. Akemann and Y. V. Fyodorov · 2003
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J. Baik P. Deift and E. Strahov · 2003
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An exact formula for general spectral correlation function of random Hermitian matrices
Y. V. Fyodorov and E. Strahov · 2003
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Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
Generalizations of Cauchy’s determinant and Schur’s Pfaffian
H. Tagawa M. Ishikawa, S. Okada and J. Zeng · 2006
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Duality in random matrix ensembles for all β \beta
P. Desrosiers · 2009
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Gromov-Witten theory, Hurwitz numbers, and matrix models
A. Okounkov and R. Pandharipande · 2009
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Duality and replicas for a unitary matrix model
E. Brézin and S. Hikami · 2010
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The Oxford handbook of random matrix theory
Gernot Akemann, Jinho Baik, and Philippe Di Francesco, editors · 2011
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Asymptotics for products of characteristic polynomials in classical β \beta -ensembles
P. Desrosiers and D.-Z. Liu · 2014
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E. Strahov and Y. V. Fyodorov · 2003
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Correlation functions of characteristic polynomials as determinants of integrable kernels: universality in the Dyson limit
E. Strahov and Y.V. Fyodorov · 2003
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Random matrices
M. L. Mehta · 2004
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Universal behavior for averages of characteristic polynomials at the origin of the spectrum
M. Vanlessen · 2005
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The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes’ phenomenon
M. Bertola and M. Cafasso
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http://dlmf.nist.gov/
NIST Digital Library of Mathematical Functions
Cited in the paper.
Darboux transformations and random point processes
M. Bertola and M. Cafasso · 2015
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Scaling limits of correlations of characteristic polynomials for the Gaussian β \beta -ensemble with external source
P. Desrosiers and D.-Z. Liu · 2015
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