Generalized Christoffel-Darboux formula for skew-orthogonal polynomials   and random matrix theory
  We obtain generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials (SOP). Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles (GOE) and Gaussian symplectic ensembles (GSE) of random matrices. 
Saugata Ghosh