Related papers: Random matrices applications to soft spectra
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
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…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the standard first-order…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…
The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems; in this situation, the modelbased methods need be revisited. A data-driven method, as…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…