  A celebrated result by Gordon allows one to compare the min-max behavior of
two Gaussian processes if certain inequality conditions are met. The
consequences of this result include the Gaussian min-max (GMT) and convex
Gaussian min-max (CGMT) theorems which have had far-reaching implications in
high-dimensional statistics, machine learning, non-smooth optimization, and
signal processing. Both theorems rely on a pair of Gaussian processes, first
identified by Slepian, that satisfy Gordon's comparison inequalities. To date,
no other pair of Gaussian processes satisfying these inequalities has been
discovered. In this paper, we identify such a new pair. The resulting theorems
extend the classical GMT and CGMT Theorems from the case where the underlying
Gaussian matrix in the primary process has iid rows to where it has independent
but non-identically-distributed ones. The new CGMT is applied to the problems
of multi-source Gaussian regression, as well as to binary classification of
general Gaussian mixture models.
