Abstract: Ben Arous and A.Guionnet gave (1995) the first large deviation result for the Gaussian Unitary ensemble.This was subsequently extended to general Unitary matrix ensembles. I will discuss a method for obtaining such results using potential theory and, time permitting,its extension to other mathematical models. This is joint work with N.Levenberg and F.Wielonsky. No prior knowledge of random matrices will be assumed.