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 …

In this article, we compute and compare the statistics of the number of eigenvalues in a
centred disc of radius R in all three Ginibre ensembles. We determine the mean and …

We consider a two-dimensional determinantal point process arising in the random normal
matrix model and which is a two-parameter generalization of the complex Ginibre point …

We consider 2-dimensional determinantal processes that are rotationinvariant and study the
fluctuations of the number of points in disks. Based on the theory of mod-phi convergence …

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 …

We investigate the construction of diffusions consisting of infinitely numerous Brownian
particles moving in R^d and interacting via logarithmic functions (two-dimensional Coulomb …

We study the Ginibre ensemble of N× N complex random matrices and compute exactly, for
any finite N, the full distribution as well as all the cumulants of the number N r of eigenvalues …

We solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite
number of Brownian particles interacting via two-dimensional Coulomb potentials. The …

The Ginibre point process (GPP) is one of the main examples of determinantal point
processes on the complex plane. It is a recurring distribution of random matrix theory as well …