Spectra of large random matrices: A method of study

A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The approach presented is equally suitable for description of both local and global spectral characteristics, thereby providing an overall look at the phenomenon of spectral universality in Random Matrix Theory.