Related papers: Random matrix theory and multivariate statistics
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…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
This paper deals with the Elliptical Wishart and Inverse Elliptical Wishart distributions, which play a major role when handling covariance matrices. Similarly to multivariate elliptical distributions, these form a large family of…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
We study the full counting statistics of current of large open systems through the application of random matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…