## 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

Zbl 1071.15027
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