Janossy Densities I. Determinantal Ensembles

摘要

We derive an elementary formula for Janossy densities for determinantal pointprocesses with a finite rank projection-type kernel. In particular, for beta=2polynomial ensembles of random matrices we show that the Janossy densities onan interval I can be expressed in terms of the Christoffel-Darboux kernel forthe orthogonal polynomials on the complement of I.