Thomas Wolfs: A derivative type for random tiling and quantum transport models

Abstract: I will show that certain random tiling and quantum transport models can be interpreted as a polynomial ensemble of derivative type. Originally, such ensembles were introduced in random matrix theory because they provide a natural framework to describe the eigenvalues of sums and products of random matrices. To make the connection to the other models, I will introduce several new notions of derivative type, either increasing the complexity of the underlying space or the associated differential operator. Afterwards, I will explain how this additional structure leads to a double integral representation for the correlation kernel of the ensemble. Such a representation then opens up the road for the asymptotic analysis of the initial models.