Gap Probabilities in Random Matrix Ensembles

Abstract: In this degree project we look at eigenvalue statistics of two randommatrix ensembles, the Gaussian and the circular ensembles. We beginwith their definition and discuss the joint probability distribution of theirentries and eigenvalues. In addition we introduce two sparse matrix models which enables us to numerically compute some eigenvalues statisticsfor these ensembles via the use of simulation. In particular we focus on thegap probability. Lastly we present and discuss the result of the numerical simulations.