Related papers: Eigenvalues of random matrices with generalised co…
It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
We study properties of eigenvalues of a matrix associated with a randomly chosen partial automorphism of a regular rooted tree. We show that asymptotically, as the numbers of levels goes to infinity, the fraction of non-zero eigenvalues…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…
We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process…
The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…
This paper focuses on large neural networks whose synaptic connectivity matrices are randomly chosen from certain random matrix ensembles. The dynamics of these networks can be characterized by the eigenvalue spectra of their connectivity…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…