Janossy Densities I. Determinantal Ensembles

Abstract

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 can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of I.

This is the first of two papers on Janossy densities in determinantal and pfaffian ensembles. A few misprints are corrected. The paper will appear in J.Stat.Phys, vol. 113, No. 3/4, pp. 595-610 (2003)