Janossy Densities I. Determinantal Ensembles
Mathematical Physics
2007-05-23 v4 math.MP
Probability
Abstract
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.
Cite
@article{arxiv.math-ph/0212063,
title = {Janossy Densities I. Determinantal Ensembles},
author = {Alexei Borodin and Alexander Soshnikov},
journal= {arXiv preprint arXiv:math-ph/0212063},
year = {2007}
}
Comments
This is the first of two papers on Janossy densities in determinantal and pfaffian ensembles. A few misprints are corrected. The paper will appear in J.Stat.Phys, vol. 113, No. 3/4, pp. 595-610 (2003)