Related papers: A new classification scheme for Random Matrix Theo…
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 provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
The paper studies ways in which the sets of a partition of a lattice in $\RR^n$ become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in $\RR^n$ gives rise to…
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper…
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
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…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of one-dimensional interacting fermions…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
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 analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD).…
The recent evidence for neutrino oscillations stimulate us to discuss again the problem of fermion masses and mixings in gauge theories. In the standard model, several forms for quark mass matrices are equivalent. They become ansatze within…
A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory in d=3, and BF theory and general…
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…