Janossy Densities of Coupled Random Matrices

We explicitly calculate the Janossy densities for a special class of finite determinantal random point processes with several types of particles introduced by Prähofer and Spohn and, in the full generality, by Johansson in connection with the analysis of polynuclear growth models. The results of this paper generalize the theorem we proved earlier with Borodin about the Janossy densities in biorthogonal ensembles. In particular our results can be applied to ensembles of random matrices coupled in a chain which provide a very important example of determinantal ensembles we study.