Quadratic Vector Equations On Complex Upper Half-Plane

DOI10.1090/memo/1261zbMath1450.15002arXiv1506.05095OpenAlexW2243692787WikidataQ126800278 ScholiaQ126800278MaRDI QIDQ5213185

László Erdős, Torben Krüger, Oskari Heikki Ajanki

Publication date: 31 January 2020

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05095

zbMATH Keywords

Stieltjes transformrandom matricesdensity of stateslocal lawalgebraic singularitycubic cuspWigner-type random matrix

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Spectrum, resolvent (47A10) Random matrices (algebraic aspects) (15B52) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02)

Related Items (29)

Local spectral statistics of Gaussian matrices with correlated entries ⋮ Edge universality of correlated Gaussians ⋮ Correlated random matrices: band rigidity and edge universality ⋮ Universality for general Wigner-type matrices ⋮ Local law and rigidity for unitary Brownian motion ⋮ Central Limit Theorem for Linear Eigenvalue Statistics of <scp>Non‐Hermitian</scp> Random Matrices ⋮ Gaussian fluctuations in the equipartition principle for Wigner matrices ⋮ Cusp universality for random matrices. I: Local law and the complex Hermitian case ⋮ Critical behavior of non-intersecting Brownian motions ⋮ Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices ⋮ Central limit theorem for linear spectral statistics of block-Wigner-type matrices ⋮ Randomly coupled differential equations with elliptic correlations ⋮ Single eigenvalue fluctuations of general Wigner-type matrices ⋮ Singular value distribution of dense random matrices with block Markovian dependence ⋮ Universality for random matrix flows with time-dependent density ⋮ The Dyson equation with linear self-energy: spectral bands, edges and cusps ⋮ Stability of the matrix Dyson equation and random matrices with correlations ⋮ On the support of the free additive convolution ⋮ No outliers in the spectrum of the product of independent non-Hermitian random matrices with independent entries ⋮ Delocalization transition for critical Erdős-Rényi graphs ⋮ Local inhomogeneous circular law ⋮ Local spectral statistics of the addition of random matrices ⋮ Bounds on the norm of Wigner-type random matrices ⋮ Local law and complete eigenvector delocalization for supercritical Erdős-Rényi graphs ⋮ Inhomogeneous circular law for correlated matrices ⋮ Universality of the least singular value for the sum of random matrices ⋮ Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices ⋮ Non-Hermitian random matrices with a variance profile. II: properties and examples ⋮ Anomalous singularity of the solution of the vector Dyson equation in the critical case

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