相关论文: Random Matrices and Supersymmetry in Disordered Sy…

Physical systems exhibiting stochastic or chaotic behavior are often amenable to treatment by random matrix models. In deciding on a good choice of model, random matrix physics is constrained and guided by symmetry considerations. The…

The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…

This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach 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…

Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…

The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…

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…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…

Power systems are developing very fast nowadays, both in size and in complexity; this situation is a challenge for Early Event Detection (EED). This paper proposes a data- driven unsupervised learning method to handle this challenge.…

In this work, we present some applications of random matrix theory for the training of deep neural networks. Recently, random matrix theory (RMT) has been applied to the overfitting problem in deep learning. Specifically, it has been shown…

In this paper, High-dimensional data analysis methods are proposed to deal with random matrix which is composed by the real data from power network before and after the fault. The mean spectral radius (MSR) of non-Hermitian random matrices…

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…

We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma…

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…

It is important for detecting the anomaly in power systems before it expands and causes serious faults such as power failures or system blackout. With the deployments of phasor measurement units (PMUs), massive amounts of synchrophasor…

It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…

This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…

In the last few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively.…

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…

We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…