Gernot Akemann – Leverhulme lecture 3

Introduction to non-hermitian random matrix theory and planar orthogonal polynomials

In these 3 lectures I will give several examples for ensembles of non-Hermitian random matricers with complex eigenvalues. Planar orthogonal polynomials will be introduced as a tool and I will show how to determine them and their kernel. Several quantities such as eigenvalue correlation functions, gap probabilities and the distribution of individual eigenvalues follow from this approach.