Correlation kernels for sums and products of random matrices

DOI10.1142/S2010326315500173zbMath1330.15040arXiv1505.00610OpenAlexW2963325207MaRDI QIDQ3459157

Tom Claeys, Dong Wang, Arno B. J. Kuijlaars

Publication date: 30 December 2015

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.00610

zbMATH Keywords

eigenvalueGaussian unitary ensembledeterminantal point processesproducts of random matricescomplex Ginibre matrixtruncated unitary matrixMeijer G-functionspolynomial ensemblessquared singular value densitysums of random matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (14)

Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition ⋮ Exact relation between singular value and eigenvalue statistics ⋮ Singular values for products of two coupled random matrices: hard edge phase transition ⋮ Propagation of singular behavior for Gaussian perturbations of random matrices ⋮ Polynomial ensembles and Pólya frequency functions ⋮ Cyclic Pólya ensembles on the unitary matrices and their spectral statistics ⋮ Averages of products and ratios of characteristic polynomials in polynomial ensembles ⋮ Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral ⋮ Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices ⋮ Spectral densities of singular values of products of Gaussian and truncated unitary random matrices ⋮ Additive matrix convolutions of Pólya ensembles and polynomial ensembles ⋮ Eigenvalue distribution of some nonlinear models of random matrices ⋮ Hard edge statistics of products of Pólya ensembles and shifted GUE's ⋮ Spectral statistics for the difference of two Wishart matrices

Uses Software

• DLMF

Cites Work

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