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 …

A number of random matrix ensembles permitting exact determination of their eigenvalue
and eigenvector statistics maintain this property under a rank 1 perturbation. Considered in …

Duality identities in random matrix theory for products and powers of characteristic
polynomials, and for moments, are reviewed. The structure of a typical duality identity for the …

We investigate the evolution of the empirical distribution of the complex roots of high-degree
random polynomials, when the polynomial undergoes the heat flow. In one prominent …

We investigate radial statistics of zeros of hyperbolic Gaussian Analytic Functions (GAF) of
the form $\varphi (z)=\sum_ {k\ge 0} c_k z^ k $ given that $|\varphi (0)|^ 2= t $ and assuming …

Complex eigenvalues of random matrices J= GUE+ i γ diag (1, 0,…, 0) provide the simplest
model for studying resonances in wave scattering from a quantum chaotic system via a …

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 provide a dynamical study of a model of multiplicative perturbation of a unitary matrix
introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound …

This thesis is structured into two parts. In the first part, we consider the random variable X:=
Tr (f1 (W) A1... fk (W) Ak) where W is an N× N Hermitian Wigner matrix, k∈ N, and we …