Computation of correlation functions and various statistical quantities of different types of Random Matrix Ensembles

We propose a method to compute correlation functions for biorthogonal random matrix ensembles with arbitrary confining potential, by inverting the associated Hankel moment-matrix. We show that using this method it is possible to calculate eigenvalue density, two-point correlation functions, gap functions and other statistical quantities of interest for a wide class of log-gas models. The method allows one to calculate such statistical quantities numerically without evaluating the relevant polynomials or generating explicit matrices. We reproduce standard results for a variety of well-known ensembles and show some new results for Muttalib-Borodin ensembles for which analytic or numerical results have not yet been obtained.