Related papers: Wishart and Anti-Wishart random matrices

Let $\a$ be a real-valued random variable of mean zero and variance 1. Let $M_n(\a)$ denote the $n \times n$ random matrix whose entries are iid copies of $\a$ and $\sigma_n(M_n(\a))$ denote the least singular value of $M_n(\a)$.…

We study the partial transposition ${W}^\Gamma=(\mathrm{id}\otimes \mathrm{t})W\in M_{dn}(\mathbb C)$ of a Wishart matrix $W\in M_{dn}(\mathbb C)$ of parameters $(dn,dm)$. Our main result is that, with $d\to\infty$, the law of $m{W}^\Gamma$…

We address overcrowding estimates for the singular values of random iid matrices, as well as for the eigenvalues of random Wigner matrices. We show evidence of long range separation under arbitrary perturbation even in matrices of discrete…

Let W be a Wishart random matrix of size d^2 times d^2, considered as a block matrix with d times d blocks. Let Y be the matrix obtained by transposing each block of W. We prove that the empirical eigenvalue distribution of Y approaches a…

Clustering time series into similar groups can improve models by combining information across like time series. While there is a well developed body of literature for clustering of time series, these approaches tend to generate clusters…

We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…

A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…

The null linear discriminant analysis method is a competitive approach for dimensionality reduction. The implementation of this method, however, is computationally expensive. Recently, a fast implementation of null linear discriminant…

In recent years the Rosenzweig--Porter (RP) ensemble, obtained by adding a diagonal matrix with independent and identically distributed elements to a Gaussian random matrix, has been widely used as a minimal model for the emergence of…

We characterize the limiting second order distributions of certain independent complex Wigner and deterministic matrices using Voiculescu's notions of freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's…

We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…

The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…

The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is…

The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…

Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…

In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with…

We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium…