Around the circular law (Q431517)

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scientific article; zbMATH DE number 6050910

Language	Label	Description	Also known as
English	Around the circular law	scientific article; zbMATH DE number 6050910

Statements

scholarly article

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Around the circular law (English)

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Charles Bordenave

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Probability Surveys

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publication date

28 June 2012

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full work available at URL

https://arxiv.org/abs/1109.3343

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https://projecteuclid.org/euclid.ps/1325604980

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zbMATH Keywords

spectrum

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singular values

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random matrices

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random graphs

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circular law

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describes a project that uses

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MaRDI profile type

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On the Marchenko-Pastur and circular laws for some classes of random matrices with dependent entries

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Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem

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Gap probabilities in non-Hermitian random matrix theory

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Asymptotics in the random assignment problem

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Processes on unimodular random networks

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An Introduction to Random Matrices

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Eigenvalues and singular values of certain random matrices

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On the roots of a random system of equations. The theorem of Shub and Smale and some extensions

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A note on the largest eigenvalue of a large dimensional sample covariance matrix

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Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang

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Limit of the smallest eigenvalue of a large dimensional sample covariance matrix

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Spectral measure of heavy tailed band and covariance random matrices

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The spectrum of heavy tailed random matrices

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Large deviations from the circular law

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Random right eigenvalues of Gaussian quaternionic matrices

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Edge scaling limits for a family of non-Hermitian random matrix ensembles

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Computation of some examples of Brown's spectral measure in free probability

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Zeros of random polynomials on \(\mathbb C^m\)

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On the spectrum of sum and product of non-Hermitian random matrices

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Circular law theorem for random Markov matrices

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Spectrum of large random reversible Markov chains: heavy-tailed weights on the complete graph

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Spectrum of non-Hermitian heavy tailed random matrices

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The Ginibre ensemble of real random matrices and its scaling limits

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On the singularity probability of discrete random matrices

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Circular law for noncentral random matrices

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The Dirichlet Markov ensemble

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Interactions between compressed sensing random matrices and high dimensional geometry

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A generalization of the Lindeberg principle

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On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices

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Eigenvalues and Condition Numbers of Random Matrices

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The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law

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How many zeros of a random polynomial are real?

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How Many Eigenvalues of a Random Matrix are Real?

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Random polynomials and expected complexity of bisection methods for real solving

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Wegner Estimate and Level Repulsion for Wigner Random Matrices

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Non-Gaussian non-Hermitian random matrix theory: phase transition and addition formalism

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Non-hermitian random matrix theory: Method of hermitian reduction

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Derivation of an eigenvalue probability density function relating to the Poincaré disk

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Determinant theory in finite factors

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Statistical Ensembles of Complex, Quaternion, and Real Matrices

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The Circular Law: ten years later

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The Strong Circular Law. Twenty years later. Part I

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The Strong Circular Law. Twenty years later. Part II

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The Circular Law. Twenty years later. Part III

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L.I.F.E.: and Halloween Law

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The palm measure and the Voronoi tessellation for the Ginibre process

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Eigenvalue curves of asymmetric tridiagonal random matrices

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The Thouless formula for random non-Hermitian Jacobi matrices

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The circular law for random matrices

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On the singular spectrum of powers and products of random matrices

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On the Distribution of Complex Roots of Random Polynomials with Heavy-tailed Coefficients

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The single ring theorem

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Convergence of the spectral measure of non-normal matrices

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Concentration of the spectral measure for large matrices

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Support convergence in the single ring theorem

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Concentration of the spectral measure of large Wishart matrices with dependent entries

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Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras

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Brown measures of unbounded operators affiliated with a finite von Neumann algebra

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On the remarkable spectrum of a non-Hermitian random matrix model

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On the Eigenvalues of a Matrix with Prescribed Singular Values

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On the Expected Number of Real Zeros of Random Polynomials I. Coefficients with Zero Means

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On the Expected Number of Real Zeros of Random Polynomials. II. Coefficients With Non-Zero Means

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Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

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From Gumbel to Tracy-Widom

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A correction to “On the average number of real roots of a random algebraic equation”

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On the average number of real roots of a random algebraic equation

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On the Average Number of Real Roots of a Random Algebraic Equation (II)

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Symmetric Random Walks on Groups

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On the spectra of Gaussian matrices

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Random analytic chaotic eigenstates.

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The concentration of measure phenomenon

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Complex Hermite polynomials: from the semi-circular law to the circular law

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Convergence to a stable distribution via order statistics

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Smallest singular value of random matrices and geometry of random polytopes

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Real Zeros of Random Polynomials

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Real Zeros of Random Polynomials. II

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Identities and Inequalities for Tree Entropy

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On the Distribution of the Number of Real Roots of Random Polynomials

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On the Variance of the Number of Real Roots of Random Polynomials

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The expected eigenvalue distribution of a large regular graph

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Some results on random circulant matrices

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Products of independent non-Hermitian random matrices

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Circular law, extreme singular values and potential theory

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On one property of Derrida-Ruelle cascades

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Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process

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General tridiagonal random matrix models, limiting distributions and fluctuations

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A limit theorem at the edge of a non-Hermitian random matrix ensemble

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Deviations from the circular law

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Gaussian fluctuations for non-Hermitian random matrix ensembles

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The Noise in the Circular Law and the Gaussian Free Field

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Universal sum and product rules for random matrices

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The Littlewood-Offord problem and invertibility of random matrices

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On the limit distributions of random matrices with independent or free entries

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Real roots of random polynomials and zero crossing properties of diffusion equation

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Expected Number of Real Zeros of a Random Polynomial with Independent Identically Distributed Symmetric Long-Tailed Coefficients

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The Complex Zeros of Random Polynomials

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The spectral radii and norms of large dimensional non-central random atrices matrices

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Random regularization of Brown spectral measure

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Algorithms and Data Structures

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Concentration of measure and isoperimetric inequalities in product spaces

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RANDOM MATRICES: THE CIRCULAR LAW

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From the Littlewood-Offord problem to the Circular Law: Universality of the spectral distribution of random matrices

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Inverse Littlewood-Offord theorems and the condition number of random discrete matrices

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Random matrices: The distribution of the smallest singular values

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Random matrices: universality of ESDs and the circular law

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The analogues of entropy and of Fisher's information measure in free probability theory. II

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Free Random Variables

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Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation

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Large Deviations of Empirical Measures of Zeros of Random Polynomials

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Matrix inequalities

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Identifiers

zbMATH Open document ID

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10.1214/11-PS183

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:431517

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