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We propose a novel method for analysis of experimental data obtained at relativistic nucleus-nucleus collisions. The method, based on the ideas of Random Matrix Theory, is applied to detect systematic errors that occur at measurements of…

High Energy Physics - Experiment · Physics 2009-11-11 E. I. Shahaliev , R. G. Nazmitdinov , A. A. Kuznetsov , M. K. Suleymanov , O. V. Teryaev

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free…

Statistical Mechanics · Physics 2017-02-01 Joël Bun , Jean-Philippe Bouchaud , Marc Potters

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…

Probability · Mathematics 2018-06-22 Ramon van Handel

In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for…

Methodology · Statistics 2023-08-07 Peiyuan Teng , Min Xu

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

Group Theory · Mathematics 2007-05-23 Jason Fulman

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…

Statistical Mechanics · Physics 2026-01-16 Mariel Kempa , Markus Kraft , Robin Steinigeweg , Jochen Gemmer , Jiaozi Wang

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…

Mathematical Physics · Physics 2009-11-30 Nicolas Orantin

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…

Statistics Theory · Mathematics 2009-07-07 Jose A. Diaz-Garcia , Ramon Gutiérrez Jáimez

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

Disordered Systems and Neural Networks · Physics 2026-05-21 Yaprak Önder , Abbas Ali Saberi , Roderich Moessner

We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our…

High Energy Physics - Lattice · Physics 2015-06-25 F. Farchioni , I. Hip , C. B. Lang

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…

Methodology · Statistics 2016-07-07 Xinyi Xu , Xing He , Qian Ai , Robert C. Qiu

The traffic behavior of University of Louisville network with the interconnected backbone routers and the number of Virtual Local Area Network (VLAN) subnets is investigated using the Random Matrix Theory (RMT) approach. We employ the…

Networking and Internet Architecture · Computer Science 2007-06-19 Viktoria Rojkova , Mehmed Kantardzic

The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…

Probability · Mathematics 2015-01-20 Igor G. Vladimirov

In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…

Mathematical Physics · Physics 2007-05-23 Ulrika Magnea

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…

Machine Learning · Computer Science 2024-05-01 Fabio A. González , Alejandro Gallego , Santiago Toledo-Cortés , Vladimir Vargas-Calderón

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…

High Energy Physics - Theory · Physics 2026-05-12 Dmitry S. Ageev , Vasilii V. Pushkarev

Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…

Statistical Mechanics · Physics 2018-03-02 Sherif M. Abuelenin

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

Numerical Analysis · Mathematics 2025-09-23 Anastasia Kireeva , Joel A. Tropp

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…

High Energy Physics - Theory · Physics 2009-10-30 Sanjay Jain

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…