Related papers: Random matrices: tail bounds for gaps between eige…
We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.
This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Lapalace…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We study the extent of independence needed to approximate the product of bounded random variables in expectation, a natural question that has applications in pseudorandomness and min-wise independent hashing. For random variables whose…
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…
In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erd\H{o}s-R\'enyi random graph $\mathcal{G}_{n,p}$, in the regime of $p$ where the edge of the spectrum is no…
We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms,…
Many solutions for scientific problems rely on finding the first (largest) eigenvalue and eigenvector of a particular matrix. We explore the distribution of the first eigenvector of a symmetric random sparse matrix. To analyze the…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding…
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)…
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…