We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with a source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a particular algebraic curve. For the case of a quartic external field, the curve in question is proven to exist, yielding precise asymptotic information about the limiting mean density of eigenvalues, as well as bulk and edge universality.
ASJC Scopus subject areas
- Applied Mathematics
- Statistical and Nonlinear Physics
- Mathematical Physics