QCD-INSPIRED SPECTRA FROM BLUES FUNCTIONS

We use the law of addition in random matrix theory to analyze the spec tral distributions of a variety of chiral random matrix models as insp ired from QCD whether through symmetries or models. In terms of the Bl ue's functions recently discussed by Zee, we show that most of the spe ctral distributions in the macroscopic limit and the quenched approxim ation, follow algebraically from the discontinuity of a pertinent solu tion to a cubic (Cardano) or a quartic (Ferrari) equation. We use the end-point equation of the energy spectra in chiral random matrix model s to argue for novel phase structures, in which the Dirac density of s tates plays the role of an order parameter.