Singular value distribution of products of random matrices

Recently, the study of products of random matrices gained a lot of interest. Motivated by this, we will be particularly focussing on three different models: (1) the product of r Ginibre random matrices, (2) the product of r truncated unitary matrices, and (3) the Laguerre Muttalib-Borodin ensemble, which was recently shown to have an interpretation in terms of products of random matrices. The squared singular values of model (1) and (2) and the eigenvalues of model (3) all form a determinantal point process on the positive half-line. To be more concrete, the density defines a biorthogonal ensemble with a very specific structure which we will call a polynomial ensemble. In this thesis we analyze the singular value (or eigenvalue) density for model (1), (2) and (3).status: publishe