Related papers: Non-Hermitian random matrices with a variance prof…

We show that for an $n\times n$ random symmetric matrix $A_n$, whose entries on and above the diagonal are independent copies of a sub-Gaussian random variable $\xi$ with mean $0$ and variance $1$, \[\mathbb{P}[s_n(A_n) \le…

We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…

Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…

We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M independent NxN Gaussian random matrices in the large-N limit is rotationally symmetric in the complex plane and is given by a simple expression rho(z,\bar{z}) =…

We consider the moment space $\mathcal{M}_n$ corresponding to $p \times p$ real or complex matrix measures defined on the interval $[0,1]$. The asymptotic properties of the first $k$ components of a uniformly distributed vector $(S_{1,n},…

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…

We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…

We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…

This paper is centred on the spectral study of a Random Fourier matrix, that is an $n\times n$ matrix $A$ whose $(j, k)$ entries are $\exp(2i\pi m X_jY_k)$, with $X_j$ and $Y_k$ two i.i.d sequences of random variables and $1\leq m\leq n$ is…

We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…

We consider the double scaling limit in the random matrix ensemble with an external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with two eigenvalues $\pm a$ of…

We prove a deterministic analogue of Rudelson's sampling theorem for sums of positive semidefinite matrices. Let $A_1,\dots,A_m$ be positive semidefinite \(d\times d\) matrices, and let $\lambda_1,\dots,\lambda_m \ge 0$ satisfy \[…

Let $F_n$ be an $n$ by $n$ symmetric matrix whose entries are bounded by $n^{\gamma}$ for some $\gamma>0$. Consider a randomly perturbed matrix $M_n=F_n+X_n$, where $X_n$ is a random symmetric matrix whose upper diagonal entries $x_{ij}$…

We study the problem of testing whether a matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ with bounded entries ($\|\mathbf{A}\|_\infty \leq 1$) is positive semi-definite (PSD), or $\epsilon$-far in Euclidean distance from the PSD cone,…

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors…

Consider the random matrix model $A^{1/2} UBU^* A^{1/2},$ where $A$ and $B$ are two $N \times N$ deterministic matrices and $U$ is either an $N \times N$ Haar unitary or orthogonal random matrix. It is well-known that on the macroscopic…

We introduce a generalized ensemble of nonhermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an…

In the past 20 years, the study of real eigenvalues of non-symmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the…

We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central…