  We study the partition functions associated with non-intersecting polymers in
a random environment. By considering paths in series and in parallel, the
partition functions carry natural notions of subadditivity, allowing the
effective study of their asymptotics. For a certain choice of random
environment, the geometric RSK correspondence provides an explicit
representation of the partition functions in terms of a stochastic interface.
Formally this leads to a variational description of the macroscopic behaviour
of the interface and hence the free energy of the associated non-intersecting
polymer model. At zero temperature we relate this variational description to
the Marchenko-Pastur distribution, and give a new derivation of the surface
tension of the bead model.
