Related papers: From random matrices to systems of particles in in…
For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…
Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction…
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…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
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 diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…