Related papers: Concentration of the Spectral Measure for Large Ra…
We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also…
The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…
In this short note we derive concentration inequalities for the empirical absolute moments of square symmetric matrices with independent symmetrically distributed +/-1 entries. Most of the previous results of this type are limited to…
We prove that few largest (and most important) eigenvalues of random symmetric matrices of various kinds are very strongly concentrated. This strong concentration enables us to compute the means of these eigenvalues with high precision. Our…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
Concentration of measure is studied, and obtained, for stable and related random vectors.
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…
We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$. Under various assumptions we establish the…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices.…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly…
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to…
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…