  We explain a unified approach to a study of ballistic phase for a large
family of self-interacting random walks with a drift and self-interacting
polymers with an external stretching force. The approach is based on a recent
version of the Ornstein-Zernike theory developed in earlier works. It leads to
local limit results for various observables (e.g. displacement of the end-point
or number of hits of a fixed finite pattern) on paths of n-step walks
(polymers) on all possible deviation scales from CLT to LD. The class of
models, which display ballistic phase in the "universality class" discussed in
the paper, includes self-avoiding walks, Domb-Joyce model, random walks in an
annealed random potential, reinforced polymers and weakly reinforced random
walks.
