Related papers: Random Discrete Matrices
This work studies the distribution of the nonsymmetric matrix $\mathbf{E}^{-1}\mathbf{H}$. This random product is of fundamental interest under the general multivariate linear hypothesis setting. Specifically when $\mathbf{H}$ and…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Results are presented from calculations carried out in the discrete QCD model, concerning multiplicity distributions in rapidity intervals and fluctuations.
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…
We study the analytic properties of a matrix discrete system introduced in [7]. The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This…
We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].
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…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…