Average characteristic polynomials for multiple orthogonal polynomial ensembles

DOI10.1016/j.jat.2009.11.008zbMath1202.42047arXiv0907.0156OpenAlexW1985683078MaRDI QIDQ976204

Steven Delvaux

Publication date: 17 June 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0156

zbMATH Keywords

Schur complementRiemann-Hilbert problemChristoffel-Darboux kerneldeterminantal point process(Block) Hankel determinantaverage characteristic polynomialmultiple/matrix orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (10)

Matrix-valued orthogonal polynomials related to hexagon tilings ⋮ Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices ⋮ A graph-based equilibrium problem for the limiting distribution of nonintersecting Brownian motions at low temperature ⋮ Critical measures on higher genus Riemann surfaces ⋮ Average characteristic polynomials of determinantal point processes ⋮ Nikishin systems are perfect. The case of unbounded and touching supports ⋮ The two-periodic Aztec diamond and matrix valued orthogonal polynomials ⋮ A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type ⋮ Correlation functions for determinantal processes defined by infinite block Toeplitz minors ⋮ Average characteristic polynomials in the two-matrix model

Cites Work

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• Moment matrices and multi-component KP, with applications to random matrix theory
• Coincidence probabilities
• Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions
• A note on biorthogonal ensembles
• On the Christoffel-Darboux kernel for random Hermitian matrices with external source
• The isomonodromy approach to matrix models in 2D quantum gravity
• Universality of correlation functions of Hermitian random matrices in an external field
• Multiple orthogonal polynomials
• Algebraic aspects of matrix orthogonality for vector polynomials
• Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach
• Biorthogonal ensembles
• Quasideterminants
• Averages of characteristic polynomials in random matrix theory
• Multiple orthogonal polynomial ensembles
• An exact formula for general spectral correlation function of random Hermitian matrices
• Products and ratios of characteristic polynomials of random Hermitian matrices
• The connection between systems of polynomials orthogonal with respect to different distribution functions
• Matrix-valued orthogonal polynomials on the real line: some extensions of the classical theory
• Characteristic polynomials of random matrices.
• Random matrix theory and \(\zeta(1/2+it)\).

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