Related papers: Application of Random Matrix Theory in High-Dimens…
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…
Large-dimensional random matrix theory, RMT for short, which originates from the research field of quantum physics, has shown tremendous capability in providing deep insights into large dimensional systems. With the fact that we have…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
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…
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
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…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
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…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where…
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…
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 the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…
We show that, within a finite window of parameter space, random matrix theory (RMT) statistics emerge in observables of a finite-volume massive free scalar field theory after a local operator quench. The spacing-ratio distribution of…