Products and ratios of characteristic polynomials of random Hermitian matrices

DOI10.1063/1.1587875zbMath1062.15014arXivmath-ph/0304016OpenAlexW1981840307MaRDI QIDQ4833082

Eugene Strahov, Jinho Baik, Percy A. Deift

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0304016

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Unnamed Item
• Discrete Painlevé equations and their appearance in quantum gravity
• Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Moments of the characteristic polynomial in the three ensembles of random matrices
• Random matrix theory and the derivative of the Riemann zeta function
• An exact formula for general spectral correlation function of random Hermitian matrices
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• The connection between systems of polynomials orthogonal with respect to different distribution functions
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
• Characteristic polynomials of random matrices.
• Random matrix theory and \(\zeta(1/2+it)\).
• On the characteristic polynomial of a random unitary matrix