Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
From MaRDI portal
Publication:1675657
DOI10.1016/j.laa.2017.09.024zbMath1376.15025arXiv1506.02017OpenAlexW2963917322MaRDI QIDQ1675657
Roland Speicher, Piotr Śniady, Serban Teodor Belinschi
Publication date: 2 November 2017
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.02017
Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)
Related Items (17)
Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach ⋮ Applications of realizations (aka linearizations) to free probability ⋮ Limiting spectral distribution of the product of truncated Haar unitary matrices ⋮ Summing free unitary Brownian motions with applications to quantum information ⋮ The Brown measure of a sum of two free random variables, one of which is triangular elliptic ⋮ Randomly coupled differential equations with elliptic correlations ⋮ Brown measures of free circular and multiplicative Brownian motions with self-adjoint and unitary initial conditions ⋮ Brown measure and asymptotic freeness of elliptic and related matrices ⋮ Inhomogeneous circular law for correlated matrices ⋮ Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices ⋮ Limiting Spectral Distributions of Sums of Products of Non-Hermitian Random Matrices ⋮ A general solution to (free) deterministic equivalents ⋮ Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices ⋮ The Brown measure of the sum of a self-adjoint element and an elliptic element ⋮ Spectral theory of sparse non-Hermitian random matrices ⋮ Random Lindblad dynamics ⋮ The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element
Cites Work
- Convergence of the largest singular value of a polynomial in independent Wigner matrices
- Free probability and random matrices
- The single ring theorem
- Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
- Noncommutative convexity arises from linear matrix inequalities
- The Lebesgue decomposition of the free additive convolution of two probability distributions
- The angular derivative of an operator-valued analytic function
- Limit laws for random matrices and free products
- Non-hermitian random matrix models
- Non-Gaussian non-Hermitian random matrix theory: phase transition and addition formalism
- Non-hermitian random matrix theory: Method of hermitian reduction
- Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
- Applications of realizations (aka linearizations) to free probability
- Random regularization of Brown spectral measure
- Invariant subspaces of the quasinilpotent DT-operator
- A new application of random matrices: \(\operatorname{Ext} (C_{\text{red}}^*(F_2))\) is not a group
- Products of independent elliptic random matrices
- Determinant theory in finite factors
- R-Diagonal Elements and Freeness With Amalgamation
- “Single ring theorem” and the disk-annulus phase transition
- Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
- Free Random Variables
- Lectures on the Combinatorics of Free Probability
- Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
- MOMENT FORMULAS FOR THE QUASI-NILPOTENT DT-OPERATOR
- Polynomials in Asymptotically Free Random Matrices
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
