Florent Benaych-Georges

activity

20042025

most citedLectures on the local semicircle law for Wigner matrices

71 citations · 258 across the 47 of their papers we have counts for

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41 papers · 1 filter

math.PR2025

Random Matrices and U-Statistics

Florent Benaych-Georges, Tomas Espana

We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showi…

math.PR2022★ 1 cited

A short proof of Ledoit-Péché's RIE formula for covariance matrices

Florent Benaych-Georges

This is a short proof of Ledoit-Péché's RIE formula for covariance matrices. The proof is based on the Stein formula, which gives a very simple way to derive the result. One of the…

math.PR2018

Eigenvectors of non normal random matrices

Florent Benaych-Georges, Ofer Zeitouni

We study the angles between the eigenvectors of a random $n \times n$ complex matrix $M$ with density $\propto e^{- n Tr V (M^{*} M)}$ and $x \mapsto V (x^{2})$ convex.…

math.PR2018

Eigenvectors of a matrix under random perturbation

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl

In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random…

math.PR2017★ 1 cited

Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs

Florent Benaych-Georges, Charles Bordenave, Antti Knowles

We consider inhomogeneous Erdős-Rényi graphs. We suppose that the maximal mean degree $d$ satisfies $d ≪ lo g n$ . We characterize the asymptotic behavior of the $n^{1 - o (1)}$ la…

math.PR2017★ 15 cited

Spectral radii of sparse random matrices

Florent Benaych-Georges, Charles Bordenave, Antti Knowles

We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erdős-Rényi graphs. Our error bounds a…

math.PR2017★ 2 cited

Empirical spectral distribution of a matrix under perturbation

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl

We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entrie…

math.PR2016

Fluctuation of matrix entries and application to outliers of elliptic matrices

Florent Benaych-Georges, Guillaume Cébron, Jean Rochet

For any family of $N \times N$ random matrices $(A_{k})_{k \in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central lim…

math.PR2016★ 71 cited

Lectures on the local semicircle law for Wigner matrices

Florent Benaych-Georges, Antti Knowles

These notes provide an introduction to the local semicircle law from random matrix theory, as well as some of its applications. We focus on Wigner matrices, Hermitian random matric…

math.PR2015

Spectral analysis of the Gram matrix of mixture models

Florent Benaych-Georges, Romain Couillet

This text is devoted to the asymptotic study of some spectral properties of the Gram matrix $W^{T} W$ built upon a collection $w_{1}, \dots, w_{n} \in R^{p}$ of random vecto…

math.PR2015★ 1 cited

Poisson statistics for matrix ensembles at large temperature

Florent Benaych-Georges, Sandrine Péché

In this article, we consider $β$ -ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\frac{1}{Z_N(β)}|Δ(λ)|^βe^{- \frac{Nβ}{…

math.PR2015

Fluctuations for analytic test functions in the Single Ring Theorem

Florent Benaych-Georges, Jean Rochet

We consider a non-Hermitian random matrix $A$ whose distribution is invariant under the left and right actions of the unitary group. The so-called Single Ring Theorem, proved by Gu…

math.PR2015

Local Single Ring Theorem

Florent Benaych-Georges

The Single Ring Theorem, by Guionnet, Krishnapur and Zeitouni, describes the empirical eigenvalue distribution of a large generic matrix with prescribed singular values, i.e. an $N…

math.PR2014

Fluctuations of linear statistics of half-heavy-tailed random matrices

Florent Benaych-Georges, Anna Maltsev

We consider a Wigner matrix $A$ with entries tail decaying as $x^{- α}$ with $2 < α < 4$ for large $x$ and study fluctuations of linear statistics $N^{- 1} Tr φ (A)$ . The beh…

math.PR2014★ 15 cited

Exponential bounds for the support convergence in the Single Ring Theorem

Florent Benaych-Georges

We consider an $n$ by $n$ matrix of the form $A = U T V$ , with $U, V$ some independent Haar-distributed unitary matrices and $T$ a deterministic matrix. We prove that for $k\sim n^{1/6…

math.PR2013★ 2 cited

GUE minors, maximal Brownian functionals and longest increasing subsequences

Florent Benaych-Georges, Christian Houdré

We present equalities in law between the spectra of the minors of a GUE matrix and some maximal functionals of independent Brownian motions. In turn, these results allow to recover…

math.PR2013

Central limit theorem for eigenvectors of heavy tailed matrices

Florent Benaych-Georges, Alice Guionnet

We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $α$ -stable laws, or adjacency…

math.PR2013

Largest eigenvalues and eigenvectors of band or sparse matrices

Florent Benaych-Georges, Sandrine Péché

In this text, we consider an N by N random matrix X such that all but o(N) rows of X have W non identically zero entries, the other rows having lass than $W$ entries (such as, for…

math.PR2013★ 9 cited

Outliers in the Single Ring Theorem

Florent Benaych-Georges, Jean Rochet

This text is about spiked models of non Hermitian random matrices. More specifically, we consider matrices of the type $A + P$ , where the rank of $P$ stays bounded as the dimension g…

math.PR2013★ 39 cited

Central limit theorems for linear statistics of heavy tailed random matrices

Florent Benaych-Georges, Alice Guionnet, Camille Male

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries…

math.PR2012

Localization and delocalization for heavy tailed band matrices

Florent Benaych-Georges, Sandrine Péché

We consider some random band matrices with band-width $N^{μ}$ whose entries are independent random variables with distribution tail in $x^{- α}$ . We consider the largest eigenvalues a…

math.PR2012

Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed or localized vectors

Florent Benaych-Georges, Thierry Cabanal-Duvillard

The celebrated Marchenko-Pastur theorem gives the asymptotic spectral distribution of sums of random, independent, rank-one projections. Its main hypothesis is that these projectio…

math.PR2011★ 2 cited

Perturbations of diagonal matrices by band random matrices

Florent Benaych-Georges, Nathanaël Enriquez

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a sym…

math.PR2011

Random right eigenvalues of Gaussian quaternionic matrices

Florent Benaych-Georges, Francois Chapon

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/ n$ . Using logarithmic potential theory, we p…