We observe that standard chiral random matrix models (ChRMM) follow fr
om the constant mode sector of the Nambu-Jona-Lasinio (NJL) models whe
ther in vacuum or matter. The ensuing thermodynamics is that of consti
tuent quarks, with mean-field universality in general. For two and thr
ee flavors new ChRMM with U-A(1) breaking are suggested. For three fla
vors a first order transition is noted, The relevance of some of the r
esults to lattice simulations in matter is discussed.