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We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…

Mesoscale and Nanoscale Physics · Physics 2009-11-07 Igor Rozhkov , Yan V. Fyodorov , Richard L. Weaver

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Methodology · Statistics 2024-12-11 Swapnaneel Bhattacharyya , Srijan Chattopadhyay , Sevantee Basu

We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…

Statistical Mechanics · Physics 2020-07-15 Lucas Sá , Pedro Ribeiro , Tomaž Prosen

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…

Statistical Mechanics · Physics 2007-05-23 John Evans , Fredrick Michael

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is…

Applied Physics · Physics 2020-08-05 Philipp del Hougne , Dmitry V. Savin , Olivier Legrand , Ulrich Kuhl

The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear…

Optics · Physics 2023-01-02 Cheng-Zhen Wang , Rodion Kononchuk , Ulrich Kuhl , Tsampikos Kottos

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

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…

Statistical Finance · Quantitative Finance 2018-09-27 Hirdesh K. Pharasi , Kiran Sharma , Anirban Chakraborti , Thomas H. Seligman

Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…

Mathematical Physics · Physics 2015-04-23 Yan V. Fyodorov , André Nock

The supersymmetric method is a powerful method for the evaluation of quenched averages in disordered systems. Among others, this method has been applied to the theory of S-matrix fluctuations, the theory of universal conductance…

High Energy Physics - Theory · Physics 2009-11-10 J. J. M. Verbaarschot

We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…

Chaotic Dynamics · Physics 2010-07-27 A. Matthew Smith , Lev Kaplan

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

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…

Chaotic Dynamics · Physics 2019-01-11 Bruno Bertini , Pavel Kos , Tomaz Prosen

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…

Chaotic Dynamics · Physics 2009-10-31 M. Glueck , A. R. Kolovsky , H. J. Korsch

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…

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…

Statistical Mechanics · Physics 2007-05-23 J. -Ch. Angles d'Auriac , J. -M. Maillard

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…

Statistical Mechanics · Physics 2013-05-29 James A. Hart , Thomas M. Antonsen , Edward Ott

The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…

Chaotic Dynamics · Physics 2011-12-07 P. Leboeuf , A. G. Monastra

Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…

Statistical Mechanics · Physics 2026-01-19 Kadir Çeven , Lukas Peinemann , Fabian Heidrich-Meisner

We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…

Chaotic Dynamics · Physics 2009-06-11 Jonathan P. Keating , Sebastian Müller