Universality in the Two Matrix Model with a Monomial Quartic and a General Even Polynomial Potential

In this paper we studied the asymptotic eigenvalue statistics of the 2 matrix model with the probability measure Z(n)(-1) exp (-n (tr(V(M-1) + W(M-2) - tau M1M2)) dM(1)dM(2), in the case where W = y(4)/4 and V is a general even polynomial. We studied the correlation kernel for the eigenvalues of the matrix M-1 in the limit as n -> infinity. We extended the results of Duits and Kuijlaars in [14] to the case when the limiting eigenvalue density for M-1 is supported on multiple intervals. The results are achieved by constructing the parametrix to a Riemann-Hilbert problem obtained in [14] with theta functions and then showing that this parametrix is well-defined for all n by studying the theta divisor.