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Janossy densities. I: Determinantal ensembles. (English) Zbl 1070.15020

Summary: 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 \(I\subset {\mathbb R}\) can be expressed in terms of the Christoffel-Darboux kernel for the orthogonal polynomials on the complement of \(I\).
For Part II, see Zbl 1071.15027.

MSC:

15B52 Random matrices (algebraic aspects)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
35Q15 Riemann-Hilbert problems in context of PDEs
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics

Citations:

Zbl 1071.15027
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