Related papers: Random matrices: tail bounds for gaps between eige…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
For ordinary matrix models, the eigenvalue probability density decays rapidly as one goes to infinity, in other words, has "short tails". This ensures that all the multiple trace correlators (multipoint moments) are convergent and…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…
In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…
In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint…
Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…
Consider a $N\times n$ random matrix $Z_n=(Z^n_{j_1 j_2})$ where the individual entries are a realization of a properly rescaled stationary gaussian random field. The purpose of this article is to study the limiting empirical distribution…
We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply these to determine the minimum number of distinct eigenvalues…
In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
We study the phenomenon of "crowding" near the largest eigenvalue $\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian Unitary Ensemble (GUE) of random matrix theory. We focus on two distinct quantities: (i) the…
This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will…
In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities,…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…