Hard edge limit of the product of two strongly coupled random matrices

DOI10.1088/0951-7715/29/12/3743zbMath1359.15030arXiv1511.09410OpenAlexW2259912123MaRDI QIDQ2958854

Eugene Strahov, Gernot Akemann

Publication date: 3 February 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.09410

zbMATH Keywords

singular valuesdeterminantal point processesMeijer \(G\)-kernelBessel-kernelinterpolating ensemblesproducts of complex random matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Other functions defined by series and integrals (33E20) Random matrices (algebraic aspects) (15B52) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Exact relation between singular value and eigenvalue statistics ⋮ 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 ⋮ Hurwitz numbers from Feynman diagrams ⋮ 2D Yang–Mills Theory and Tau Functions ⋮ Hurwitz numbers and products of random matrices ⋮ 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 ⋮ 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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• Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
• Gaussian ensembles of random Hermitian matrices intermediate between orthogonal and unitary ones
• A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics
• Level spacing distributions and the Bessel kernel
• Integrable Fredholm operators and dual isomonodromic deformations
• The spectrum edge of random matrix ensembles.
• Almost-Hermitian random matrices: Eigenvalue density in the complex plane
• Universality conjecture and results for a model of several coupled positive-definite matrices
• From Gumbel to Tracy-Widom
• Cauchy-Laguerre two-matrix model and the Meijer-\(G\) random point field
• Dropping the independence: singular values for products of two coupled random matrices
• Differential equations for singular values of products of Ginibre random matrices
• Energy correlations for a random matrix model of disordered bosons
• Generalized Ensemble of Random Matrices
• Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue Statistics
• Singular value correlation functions for products of Wishart random matrices
• Recent Exact and Asymptotic Results for Products of Independent Random Matrices
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS
• The Cauchy two-matrix model

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