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 …

The correlation structure of a stock market contains important financial contents, which may
change remarkably due to the occurrence of financial crisis. We perform a comparative …

The statistics of the smallest eigenvalue of Wishart–Laguerre ensemble is important from
several perspectives. The smallest eigenvalue density is typically expressible in terms of …

This chapter is based on the lectures delivered at the Les Houches Summer School in July
2015. They are addressed at a mixed audience of physicists and mathematicians with some …

Correlation functions involving products and ratios of half-integer powers of characteristic
polynomials of random matrices from the Gaussian orthogonal ensemble (GOE) frequently …

We study the probability density function (PDF) of the smallest eigenvalue of Laguerre–
Wishart matrices W= X† X where X is a random M× N (M≥ N) matrix, with complex Gaussian …

The statistical behaviour of the smallest eigenvalue has important implications for systems
which can be modeled using a Wishart–Laguerre ensemble, the regular one or the fixed …

We determine the joint probability density function (JPDF) of reflection eigenvalues in three
Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world …

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 …