Hyperuniform states of matter are correlated systems that are characterized by an
anomalous suppression of long-wavelength (ie, large-length-scale) density fluctuations …

This review covers recent results concerning the estimation of large covariance matrices
using tools from Random Matrix Theory (RMT). We introduce several RMT methods and …

The field of random matrix theory has seen an explosion of activity in recent years, with
connections to many areas of mathematics and physics. However, this makes the current …

These notes were written for the course APC 550: Probability in High Dimension that I taught
at Princeton in the Spring 2014 and Fall 2016 semesters. The aim was to introduce in as …

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …

Consider N× N Hermitian or symmetric random matrices H with independent entries, where
the distribution of the (i, j) matrix element is given by the probability measure νij with zero …

arxiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 1 Lectures on Coulomb and Riesz Gases
Sylvia Serfaty arxiv:2407.21194v1 [math-ph] 30 Jul 2024 Page 2 Page 3 Contents Preface 5 …

We consider the ensemble of adjacency matrices of Erdős–Rényi random graphs, that is,
graphs on N vertices where every edge is chosen independently and with probability …