Janossy Densities of Coupled Random Matrices

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