Universality conjecture and results for a model of several coupled positive-definite matrices

DOI10.1007/s00220-015-2327-7zbMath1318.15018arXiv1407.2597OpenAlexW2090365946WikidataQ123201253 ScholiaQ123201253MaRDI QIDQ2346846

Marco Bertola, Thomas Bothner

Publication date: 4 June 2015

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

Full work available at URL: https://arxiv.org/abs/1407.2597

zbMATH Keywords

Riemann-Hilbert problemcorrelation functionbiorthogonal polynomialsMeijer \(G\)-functionCauchy chain matrix modelCauchy-Laguerre three matrix

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Positive matrices and their generalizations; cones of matrices (15B48) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (18)

Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition ⋮ Global rigidity and exponential moments for soft and hard edge point processes ⋮ Dropping the independence: singular values for products of two coupled random matrices ⋮ Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation ⋮ A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels ⋮ Hard edge limit of the product of two strongly coupled random matrices ⋮ The matching condition for larger size Riemann-Hilbert problems ⋮ Unnamed Item ⋮ On the peakon inverse problem for the Degasperis-Procesi equation ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ 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 multiplicative constant for the Meijer-G kernel determinant ⋮ 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 ⋮ On the convergence of multi-level Hermite-Padé approximants ⋮ Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure

Uses Software

• DLMF

Cites Work

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