Dropping the independence: singular values for products of two coupled random matrices

DOI10.1007/s00220-016-2653-4zbMath1351.15020arXiv1504.02047OpenAlexW3105119160MaRDI QIDQ2630731

Eugene Strahov, Gernot Akemann

Publication date: 21 July 2016

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

Full work available at URL: https://arxiv.org/abs/1504.02047

zbMATH Keywords

eigenvaluecentral limit theoremGaussian random matricessingular valuesbiorthogonal polynomialsGinibre ensembleChristoffel-Darboux formulaLaguerre ensembleMeijer \(G\)-functions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) 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 (15)

Exact relation between singular value and eigenvalue statistics ⋮ Dynamical correlation functions for products of random matrices ⋮ Singular values for products of two coupled random matrices: hard edge phase transition ⋮ Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices ⋮ A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality ⋮ Hard edge limit of the product of two strongly coupled random matrices ⋮ 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 ⋮ Integrable structure of products of finite complex Ginibre random matrices ⋮ Product matrix processes for coupled multi-matrix models and their hard edge scaling limits ⋮ The local universality of Muttalib–Borodin biorthogonal ensembles with parameter $\theta = \frac{1}{2}$ ⋮ The local universality of Muttalib–Borodin ensembles when the parameter θ is the reciprocal of an integer ⋮ A vector Riemann-Hilbert approach to the Muttalib-Borodin ensembles ⋮ Large \(n\) limit for the product of two coupled random matrices ⋮ Spectral statistics for the difference of two Wishart matrices

Uses Software

• DLMF

Cites Work

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