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 …

We give simple criteria to identify the exponential order of magnitude of the absolute value of
the determinant for wide classes of random matrix models, not requiring the assumption of …

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian
distribution have many applications in coding, communications, signal processing and …

Let A_n be an n by n random matrix whose entries are independent real random variables
with mean zero, variance one and with subexponential tail. We show that the logarithm of …

In this paper, we survey some recent progress on rigorously establishing the universality of
various spectral statistics of Wigner Hermitian random matrix ensembles, focusing on the …

The idea of writing this book entitled “Cognitive Networked Sensing and Big Data” started
with the plan to write a briefing book on wireless distributed computing and cognitive …

We establish a central limit theorem for the log-determinant log| det (Mn)| of a Wigner matrix
Mn, under the assumption of four matching moments with either the GUE or GOE ensemble …

We prove that the logarithm of the determinant of a Wigner matrix satisfies a central limit
theorem in the limit of large dimension. Previous results about fluctuations of such …

We study $ k $-point correlators of characteristic polynomials in non-Hermitian ensembles of
random matrices, focusing on the real, complex and quaternion $ N\times N $ Ginibre …

In an isolated quantum many-body system undergoing unitary evolution, we study the
thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the …