Abstract
We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for β=2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I ⊂ ℝ can be expressed in terms of the Christoffel–Darboux kernel for the orthogonal polynomials on the complement of I.
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Borodin, A., Soshnikov, A. Janossy Densities. I. Determinantal Ensembles. Journal of Statistical Physics 113, 595–610 (2003). https://doi.org/10.1023/A:1026025003309
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DOI: https://doi.org/10.1023/A:1026025003309