Related papers: Matrix regularizing effects of Gaussian perturbati…

We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form $Y_i = \sum_j H_{ij} X_j + Z_i$, where $Y_i$ ,$X_j$ and $Z_i$ are complex, $i=1..m$, $j=1..n$, and $H$ is a…

We consider a diffusive matrix process $(X_t)_{t\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the "external source" that one would…

Let $A\in\mathbb{C}^{n\times n}$ be a normal matrix with spectrum $\{\lambda_{i}\}_{i=1}^{n}$, and let $\widetilde{A}=A+E\in\mathbb{C}^{n\times n}$ be a perturbed matrix with spectrum $\{\widetilde{\lambda}_{i}\}_{i=1}^{n}$. If…

Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…

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…

We provide a general formula for the eigenvalue density of large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and…

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a…

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…

We study the Gaussian hermitian random matrix ensemble with an external matrix which has an arbitrary number of eigenvalues with arbitrary multiplicity. We compute the limiting eigenvalues correlations when the size of the matrix goes to…

Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…

We observe that given two (compatible) classes of functions $\mathcal{F}$ and $\mathcal{H}$ with small capacity as measured by their uniform covering numbers, the capacity of the composition class $\mathcal{H} \circ \mathcal{F}$ can become…

Injecting gaussian noise into training features is well known to have regularization properties. This paper considers noise injections to numeric or categoric tabular features as passed to inference, which translates inference to a…

Given a matrix $A \in \mathbb{R}^{m\times d}$ with singular values $\sigma_1\geq \cdots \geq \sigma_d$, and a random matrix $G \in \mathbb{R}^{m\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive new bounds on the Frobenius…

The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…

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)…

We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…

We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…

Hermitian operators with exact zero modes subject to non-Hermitian perturbations are considered. Specific focus is on the average distribution of the initial zero modes of the Hermitian operators. The broadening of these zero modes is found…

We consider large-dimensional Hermitian or symmetric random matrices of the form $W=M+\vartheta V$ where $M$ is a Wigner matrix and $V$ is a real diagonal matrix whose entries are independent of $M$. For a large class of diagonal matrices…

Let $A\in\mathbb{C}^{n\times n}$ and $\widetilde{A}\in\mathbb{C}^{n\times n}$ be two normal matrices with spectra $\{\lambda_{i}\}_{i=1}^{n}$ and $\{\widetilde{\lambda}_{i}\}_{i=1}^{n}$, respectively. The celebrated Hoffman--Wielandt…