Related papers: Limiting Empirical Spectral Distribution for Produ…

We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The…

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. Two recent…

Consider two types of products of independent random matrices, including products of Ginibre matrices and inverse Ginibre matrices and products of truncated Haar unitary matrices and inverse truncated Haar matrices. Each product matrix has…

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the…

For fixed $m > 1$, we study the product of $m$ independent $N \times N$ elliptic random matrices as $N$ tends to infinity. Our main result shows that the empirical spectral distribution of the product converges, with probability $1$, to the…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…

We consider products of independent random matrices with independent entries. The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let $X^{(\nu)}_{jk},{}1\le j,r\le n$, $\nu=1,...,m$ be…

Consider the product $X = X_{1}\cdots X_{m}$ of $m$ independent $n\times n$ iid random matrices. When $m$ is fixed and the dimension $n$ tends to infinity, we prove Gaussian limits for the centered linear spectral statistics of $X$ for…

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…

We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…

For fixed $m>1$, we consider $m$ independent $n \times n$ non-Hermitian random matrices $X_1, ..., X_m$ with i.i.d. centered entries with a finite $(2+\eta)$-th moment, $ \eta>0.$ As $n$ tends to infinity, we show that the empirical…

We consider the products of $m\ge 2$ independent large real random matrices with independent vectors $(X_{jk}^{(q)},X_{kj}^{(q)})$ of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)}$ are correlated with $\rho=\mathbb E…

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…

Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…

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…

The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…

This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

We study the densities of limiting distributions of squared singular values of high-dimensional matrix products composed of independent complex Gaussian (complex Ginibre) and truncated unitary matrices which are taken from Haar distributed…