Lectures on Coulomb and Riesz gases

TL;DR

This book provides an in-depth exploration of Coulomb and Riesz gases, covering theoretical foundations and applications, based on graduate course notes and summer school lectures.

Contribution

It compiles and synthesizes advanced knowledge on Coulomb and Riesz gases, serving as a comprehensive resource for researchers and students.

Findings

Summarizes key properties of Coulomb and Riesz gases

Provides new insights into their mathematical structure

Connects theory with applications in physics and probability

Abstract

This is the preliminary version of a book on Coulomb and Riesz gases that grew out of a set of notes written for graduate courses taught at the Courant Institute, at the Ecole Normale Sup\'erieure, and at the 2024 Saint-Flour Probability summer school.