Janossy Densities I. Determinantal Ensembles

Details Janossy Densities I. Determinantal Ensembles Janossy Densities I. Determinantal Ensembles

2002-12-20

arxiv.org/abs/math-ph/0212063v4

Physics

Mathematical Physics

This is the first of two papers on Janossy densities in determinantal and pfaffian ensembles. A few misprints are corrected. T

Scientific paper

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.

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