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We establish the joint $*$-convergence of a random circulant matrix and a specific deterministic diagonal matrix. We also show that the empirical spectral distributions of skew-circulant and left skew-circulant random matrices converge…
It is shown that if a probability measure $\nu$ is supported on a closed subset of $(0,\infty)$, that is, its support is bounded away from zero, then the free multiplicative convolution of $\nu$ and the semicircle law is absolutely…
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…
We study the properties of the eigenvalues of real random matrices and their products. It is known that when the matrix elements are Gaussian-distributed independent random variables, the fraction of real eigenvalues tends to unity as the…
We establish the universality of the singular numbers in random matrix products over $\mathrm{GL}_n(\mathbb{Q}_p)$ as the number of products approaches infinity, with a fixed $n\ge 1$. We demonstrate that, under a broad class of…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there…
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 asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…
For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…
For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting…
It is well known that the spectral measure of eigenvalues of a rescaled square non-Hermitian random matrix with independent entries satisfies the circular law. We consider the product $TX$, where $T$ is a deterministic $N\times M$ matrix…
We consider products of independent square non-Hermitian random matrices. More precisely, let X(1),...,X(n) be random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with…
This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…
Products of random matrix products of $\mathrm{SL}(2,\mathbb{R})$, corresponding to transfer matrices for the one-dimensional Schr\"odinger equation with a random potential $V$, are studied. I consider both the case where the potential has…
We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…
In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the $N\times N$ truncated Hilbert matrix for large values of $N$. In this paper, we extend this formula to Hankel matrices with symbols in the class of…