Biorthogonal Polynomials for Potentials of two Variables and External Sources at the Denominator

In several domains of physics like, for instance, in string theory [1] and in quantum chromodynamics [2] we are interested in the spectral properties of random matrices; most results in this domain are included in the correlation functions for the invariants of the matrices like determinants, traces...Although most interesting results are expected from infinitely large matrices, exact results can be obtained in appropriate cases for finite matrices using the technique of orthogonal polynomials. The appropriate cases are when the integrals over the matrix elements can be transformed into integrals over the eigenvalues of the matrices; this is the case for hermitian matrices where a unitary transformation reduces the integrals to the real line for each eigenvalue. When the matrices are complex, there exists a small class of potentials [3] (which includes the Gaussian potential) where the integration can be reduced to the complex plane