We consider a planar Coulomb gas ensemble of size $ N $ with the inverse temperature
$\beta= 2$ and external potential $ Q (z)=| z|^ 2-2c\log| za| $, where $ c> 0$ and …

Random matrix theory has been widely applied in physics, and even beyond physics. Here,
we apply such tools to study catastrophic events, which occur rarely but cause devastating …

Wishart random matrix theory is of major importance for the analysis of correlated time
series. The distribution of the smallest eigenvalue for Wishart correlation matrices is …

The sum of independent Wishart matrices, taken from distributions with unequal covariance
matrices, plays a crucial role in multivariate statistics, and has applications in the fields of …

Rectangular real N×(N+ ν) matrices W with a Gaussian distribution appear very frequently in
data analysis, condensed matter physics, and quantum field theory. A central question …

Data sets collected at different times and different observing points can possess correlations
at different times and at different positions. The doubly correlated Wishart model takes both …

We consider rectangular random matrices of size× pn belonging to the real Wishart–
Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This …

Let be a single-spiked Wishart matrix in the class with, where is the identity matrix, is an
arbitrary vector with unit Euclidean norm, is a non-random parameter, and represents the …

We calculate the k-point generating function of the correlated Jacobi ensemble using
supersymmetric methods. We use the result for complex matrices for k= 1 k= 1 to derive a …

The correlated Wishart model provides a standard tool for the analysis of correlations in a
rich variety of systems. Although much is known for complex correlation matrices, the …