Janossy Densities of Coupled Random Matrices

TL;DR

This paper derives explicit formulas for Janossy densities in a class of determinantal point processes, extending previous results and applying to coupled random matrices in growth models.

Contribution

It generalizes earlier theorems on Janossy densities to include coupled random matrices and multiple particle types in determinantal point processes.

Findings

Explicit Janossy densities for special determinantal processes

Extension of previous biorthogonal ensemble results

Application to coupled random matrices in growth models

Abstract

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.