Related papers: Random unistochastic matrices
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product $P_m$ of $m$…
We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble,…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…
Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian…
We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for $\ell_p$ norms via real interpolation.
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we…
Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal…