Perfect Matchings in Inhomogeneous Random Bipartite Graphs in Random Environment

In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erd"os-R'enyi random graphs in a random environment. We show that the expected number of perfect matchings obeys a precise quenched asymptotic and that it can be approximated using an iterative process that converges exponentially fast.