  The first paper in this series introduced a new family of nonasymptotic
matrix concentration inequalities that sharply capture the spectral properties
of very general Gaussian (as well as non-Gaussian) random matrices in terms of
an associated noncommutative model. These methods achieved matching upper and
lower bounds for smooth spectral statistics, but only provided upper bounds for
the spectral edges. Here we obtain matching lower bounds for the spectral
edges, completing the theory initiated in the first paper. The resulting
two-sided bounds enable the study of applications that require an exact
determination of the spectral edges to leading order, which is fundamentally
beyond the reach of classical matrix concentration inequalities. To illustrate
their utility, we undertake a detailed study of phase transition phenomena for
spectral outliers of nonhomogeneous random matrices.
