Related papers: Summing free unitary random matrices
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of "homogenization" for Dyson Brownian Motion, this yields the universality of quantities which depend on…
This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
We review the state of the art of the theory of Euclidean random matrices, focusing on the density of their eigenvalues. Both Hermitian and non-Hermitian matrices are considered and links with simpler, standard random matrix ensembles are…
We provide a refined combinatorial identity for the set of partitions of $\{1,\dots, n\}$, which plays an important role in investigating several limit theorems related to finite free convolutions. Firstly, we present the finite free…
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e.…
We prove a universal limit theorem for the halting time, or iteration count, of the power/inverse power methods and the QR eigenvalue algorithm. Specifically, we analyze the required number of iterations to compute extreme eigenvalues of…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a…
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…
Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability…
Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…
Consider the empirical spectral distribution of complex random $n\times n$ matrix whose entries are independent and identically distributed random variables with mean zero and variance $1/n$. In this paper, via applying potential theory in…