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 …

This is part II of a review relating to the three classes of random non-Hermitian Gaussian
matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre …

We consider random normal matrix and planar symplectic ensembles, which can be
interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian …

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 consider a two-dimensional equilibrium measure problem under the presence of
quadratic potentials with a point charge and derive the explicit shape of the associated …

The one-component Coulomb gas on the sphere, consisting on $ N $ unit charges
interacting via a logarithmic potential, and in the presence of two external charges each of …

Consider the subspace W n of L 2 (C, d A) consisting of all weighted polynomials W (z)= P
(z)· e-1 2 n Q (z), where P (z) is a holomorphic polynomial of degree at most n-1, Q (z)= Q (z …

We study a class of radially symmetric Coulomb gas ensembles at inverse temperature
$\beta= 2$, for which the droplet consists of a number of concentric annuli, having at least …

We consider determinantal Coulomb gas ensembles with a class of discrete rotational
symmetric potentials whose droplets consist of several disconnected components. Under the …

We study expectations of powers and correlation functions for characteristic polynomials of
non-Hermitian random matrices. For the-point and-point correlation function, we obtain …