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Janossy Densities. I. Determinantal Ensembles |
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| Authors: | Alexei Borodin Alexander Soshnikov |
| Institution: | (1) Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York, 10012-1185;(2) Department of Mathematics, University of California at Davis, One Shields Avenue, Davis, California, 95616 |
| Abstract: | We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for  =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. |
| Keywords: | Random matrices orthogonal polynomials Janossy densities Riemann– Hilbert problem |
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