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 …

The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

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 …

Random matrix theory is now a big subject with applications in many disciplines of science,
engineering and finance. This article is a survey specifically oriented towards the needs and …

The purpose of this paper is to put forward the claim that Hurwitz's paper [Über die
Erzeugung der invarianten durch integration, Nachr. Ges. Wiss. Göttingen 1897 (1897) 71 …

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 …

It has been remarked that a fair measure of the impact of Atle Selberg's work is the number
of mathematical terms that bear his name. One of these is the Selberg integral, an $ n …

This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

Orthogonal polynomials on the real line (OPRL) were developed in the nineteenth century
and orthogonal polynomials on the unit circle (OPUC) were initially developed around 1920 …

In this article, we investigate the extremal values of (the logarithm of) the characteristic
polynomial of a random unitary matrix whose spectrum is distributed according to the …