The Dyson equation with linear self-energy: spectral bands, edges and cusps
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Publication:2205221
DOI10.25537/dm.2020v25.1421-1539zbMath1450.60005arXiv1804.07752MaRDI QIDQ2205221
László Erdős, Johannes Alt, Torben Krüger
Publication date: 20 October 2020
Published in: Documenta Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1804.07752
Stieltjes transformeigenvalue distributionDyson equationpositive operator-valued measureband rigidity
Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54)
Related Items (19)
On the deformed Pearcey determinant ⋮ Large deviations for the largest eigenvalue of matrices with variance profiles ⋮ Asymptotics of Fredholm determinant associated with the Pearcey kernel ⋮ Correlated random matrices: band rigidity and edge universality ⋮ Berry-Esseen bounds for the multivariate ℬ-free CLT and operator-valued matrices ⋮ Local law and rigidity for unitary Brownian motion ⋮ Matrix concentration inequalities and free probability ⋮ Central Limit Theorem for Linear Eigenvalue Statistics of <scp>Non‐Hermitian</scp> Random Matrices ⋮ Gaussian fluctuations in the equipartition principle for Wigner matrices ⋮ Boundary asymptotics of non-intersecting Brownian motions: Pearcey, Airy and a transition ⋮ The free field: realization via unbounded operators and Atiyah property ⋮ Randomly coupled differential equations with elliptic correlations ⋮ Quenched universality for deformed Wigner matrices ⋮ Dyson Brownian motion for general \(\beta\) and potential at the edge ⋮ On the support of the free additive convolution ⋮ Inhomogeneous circular law for correlated matrices ⋮ Quadratic Vector Equations On Complex Upper Half-Plane ⋮ Thermalisation for Wigner matrices ⋮ Anomalous singularity of the solution of the vector Dyson equation in the critical case
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