Singular values for products of two coupled random matrices: hard edge phase transition

DOI10.1007/s00365-017-9389-zzbMath1429.60013arXiv1602.00634OpenAlexW3105830002MaRDI QIDQ1647957

Dang-Zheng Liu

Publication date: 27 June 2018

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00634

zbMATH Keywords

phase transitionproducts of random matricesbi-orthogonal ensembleshard edge limitMeijer G-kernel

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Related Items

Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices ⋮ Product matrix processes for coupled multi-matrix models and their hard edge scaling limits ⋮ Hard edge statistics of products of Pólya ensembles and shifted GUE's ⋮ Large \(n\) limit for the product of two coupled random matrices

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition
• Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
• Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
• Bulk and soft-edge universality for singular values of products of Ginibre random matrices
• Limits for circular Jacobi beta-ensembles
• Total positivity, spherical series, and hypergeometric functions of matrix argument
• Universal wide correlators in non-Gaussian orthogonal, unitary and symplectic random matrix ensembles
• A new chiral two-matrix theory for Dirac spectra with imaginary chemical potential
• A note on biorthogonal ensembles
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
• The limiting empirical measure of multiple discriminant ratios
• Level spacing distributions and the Bessel kernel
• Biorthogonal ensembles
• The spectrum edge of random matrix ensembles.
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• Cauchy-Laguerre two-matrix model and the Meijer-\(G\) random point field
• The special functions and their approximations. Vol. I, II
• Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
• Dropping the independence: singular values for products of two coupled random matrices
• Asymptotic Approximations of Integrals
• Gaussian perturbations of hard edge random matrix ensembles
• Universality and critical behaviour in the chiral two-matrix model
• Differential equations for singular values of products of Ginibre random matrices
• Singular values of products of random matrices and polynomial ensembles
• Hard edge limit of the product of two strongly coupled random matrices
• Singular Values of Products of Ginibre Random Matrices
• Transformations of Polynomial Ensembles
• Eigenvalue statistics for product complex Wishart matrices
• Induced Ginibre ensemble of random matrices and quantum operations
• Differential Operators on a Semisimple Lie Algebra
• Asymptotic correlations for Gaussian and Wishart matrices with external source
• Correlation kernels for sums and products of random matrices
• An Introduction to Random Matrices
• Random Matrix Ensembles with Singularities and a Hierarchy of Painlevé III Equations
• Singular Value Statistics of Matrix Products with Truncated Unitary Matrices
• Matrices coupled in a chain: I. Eigenvalue correlations
• The planar approximation. II
• An Itzykson–Zuber-like integral and diffusion for complex ordinary and supermatrices
• Singular value correlation functions for products of Wishart random matrices
• Recent Exact and Asymptotic Results for Products of Independent Random Matrices
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Some Non-Central Distribution Problems in Multivariate Analysis
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS