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 Ginibre unitary ensemble (GinUE) consists of $ N\times N $ random matrices with
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …

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 present a brief survey of fluctuations and large deviations of particle systems with
subextensive growth of the variance. These are called hyperuniform (or …

The persistent homology of a stationary point process on RN is studied in this paper. As a
generalization of continuum percolation theory, we study higher dimensional topological …

Abstract We prove a Central Limit Theorem for the linear statistics of two-dimensional
Coulomb gases, with arbitrary inverse temperature and general confining potential, at the …

This open access book focuses on the Ginibre ensembles that are non-Hermitian random
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …

For a locally finite point set Λ ⊂ R Λ⊂ R, consider the collection of exponential functions
given by E _ Λ:={e^ i λ x: λ ∈ Λ\} E Λ:= ei λ x: λ∈ Λ. We examine the question whether E _ Λ …

A point process is said to be rigid if for any bounded domain in the phase space, the number
of particles in the domain is almost surely determined by the restriction of the configuration to …

We develop a general framework to study hyperuniformity of various mathematical models of
quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals …