The temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two space dimensions with "asymmetric" Fermi surfaces have nonzero radius of convergence. One consequence of the convergence is the existence of a discontinuity in the particle number density at the Fermi surface. In this talk, I intend to introduce the models, sketch the main results and then introduce the renormalization group map, which provides both the intuition and the framework for the proof.