Related papers: Random-matrix theory and complex atomic spectra
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…
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
The breadth of Eugene Wigner's interests and contributions is amazing and humbling. At different times in his life he did seminal work in areas as diverse as pure mathematics and chemical engineering. His seminal research in physics is, of…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
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…
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
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…