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 study products of random matrices in the regime where the number of terms and the size
of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the ℓ …

We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …

The constant modulus constraint is widely used in analog beamforming, hybrid
beamforming, intelligent reflecting surface design, and radar waveform design. The …

An exact map was established by Lacroix-A-Chez-Toine et al. in (Phys Rev A 99 (2):
021602, 2019) between the N complex eigenvalues of complex non-Hermitian random …

We study the competition between Haar-random unitary dynamics and measurements for
unstructured systems of qubits. For projective measurements, we derive various properties …

It has been shown by Akemann, Ipsen and Kieburg that the squared singular values of
products of M rectangular random matrices with independent complex Gaussian entries are …

Products of M iid random matrices of size N× N are related to classical limit theorems in
probability theory (N= 1 and large M), to Lyapunov exponents in dynamical systems (finite N …

Abstract Systems where time evolution follows a multiplicative process are ubiquitous in
physics. We study a toy model for such systems where each time step is given by …

We derive upper and lower bounds on the expectation of f(S) under dependence
uncertainty, that is, when the marginal distributions of the random vector S=(S_1,...,S_d) are …