NON-HERMITIAN RANDOM-MATRIX MODELS

We introduce an extension of the diagrammaric rules in random matrix t heory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one- and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues , while the two-point functions characterize their macroscopic correla tions, The generic form for the two-point functions is obtained, gener alizing the concept of macroscopic universality to non-hermitian rando m matrices, We show that the holomorphic and non-holomorphic one-and t wo-point functions condition the behavior of pertinent partition funct ions to order O(1/N), We derive explicit conditions for the location a nd distribution of their singularities, Most of our analytical results are found to be in good agreement with numerical calculations using l arge ensembles of complex matrices. (C) 1997 Elsevier Science B.V.