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 …

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 study Coulomb gases in any dimension d\geq2 and in a broad temperature regime. We
prove local laws on the energy, separation and number of points down to the microscopic …

We investigate the thermodynamic limit of the circular long-range Riesz gas, a system of
particles interacting pairwise through an inverse power kernel. We show that after rescaling …

We study the long-range one-dimensional Riesz gas on the circle, a continuous system of
particles interacting through a Riesz (ie inverse power) kernel. We establish near-optimal …

We investigate Sine β, the universal point process arising as the thermodynamic limit of the
microscopic scale behavior in the bulk of one‐dimensional log‐gases, or β‐ensembles, at …

We consider a periodic Riesz gas consisting of $ N $ classical particles on a circle,
interacting via a two-body repulsive potential which behaves locally as a power law of the …

For an inverse temperature β> 0, we define the β-circular Riesz gas on R d as any
microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the …

We develop a theory of optimal transport for stationary random measures with a focus on
stationary point processes and construct a family of distances on the set of stationary …

We prove, for any, a central limit theorem for the fluctuations of linear statistics in the
process, which is the infinite volume limit of the random microscopic behavior in the bulk of …