Related papers: Total variation approximation of random orthogonal…

In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…

We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…

We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…

We consider the detection problem of correlations in a $p$-dimensional Gaussian vector, when we observe $n$ independent, identically distributed random vectors, for $n$ and $p$ large. We assume that the covariance matrix varies in some…

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…

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…

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.

Let $A$ be an $n\times n$ random matrix with independent rows $R_1(A),\dots,R_n(A)$, and assume that for any $i\leq n$ and any three-dimensional linear subspace $F\subset {\mathbb R}^n$ the orthogonal projection of $R_i(A)$ onto $F$ has…

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…

We study the model of random permutations of $n$ objects with polynomially growing cycle weights, which was recently considered by Ercolani and Ueltschi, among others. Using saddle-point analysis, we prove that the total variation distance…

This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…

In this note, we study the Gaussian fluctuations for the Wishart matrices $d^{-1}\mathcal{X}_{n, d}\mathcal{X}^{T}_{n, d}$, where $\mathcal{X}_{n, d}$ is a $n\times d$ random matrix whose entries are jointly Gaussian and correlated with row…

Let ${\Gamma}_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let ${ Z}_n$ be the $p\times q$ upper-left submatrix of ${\Gamma}_n$ and ${G}_n$ be a $p\times q$ matrix whose $pq$ entries are independent standard normals, where $p$ and…

In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…

For a Haar random set $\mathcal{S}\subset U(d)$ of quantum gates we consider the uniform measure $\nu_\mathcal{S}$ whose support is given by $\mathcal{S}$. The measure $\nu_\mathcal{S}$ can be regarded as a…

We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in…

We determine the asymptotics for the variance of the number of zeros of random linear combinations of orthogonal polynomials of degree $\leq n$ in subintervals $\left [ a,b\right ] $ of the support of the underlying orthogonality measure…

Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.