Related papers: Joint distributions of eigenvectors of symmetric r…
In this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also…
We study operators obtained by coupling an $n \times n$ random matrix from one of the Gaussian ensembles to the discrete Laplacian. We find the joint distribution of the eigenvalues and resonances of such operators. This is one of the…
We show that some of the best-known matrix decompositions of some of the best-known random matrix ensembles give us the unique $G$-invariant uniform distributions on some of the best-known manifolds. The eigenvectors distributions of the…
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions.…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging,…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eigenschemes of general ternary symmetric tensors and we…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute…
Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…
We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…