Janossy densities. I. Determinantal ensembles

摘要

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for beta = 2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I subset of R can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I. [References: 32]