  The generic chaining method provides a sharp description of the suprema of
many random processes in terms of the geometry of their index sets. The
chaining functionals that arise in this theory are however notoriously
difficult to control in any given situation. In the first paper in this series,
we introduced a particularly simple method for producing the requisite multi
scale geometry by means of real interpolation. This method is easy to use, but
does not always yield sharp bounds on chaining functionals. In the present
paper, we show that a refinement of the interpolation method provides a
canonical mechanism for controlling chaining functionals. The key innovation is
a simple but powerful contraction principle that makes it possible to
efficiently exploit interpolation. We illustrate the utility of this approach
by developing new dimension-free bounds on the norms of random matrices and on
chaining functionals in Banach lattices. As another application, we give a
remarkably short interpolation proof of the majorizing measure theorem that
entirely avoids the greedy construction that lies at the heart of earlier
proofs.
