  We study quenched distributions on random walks in a random potential on
integer lattices of arbitrary dimension and with an arbitrary finite set of
admissible steps. The potential can be unbounded and can depend on a few steps
of the walk. Directed, undirected and stretched polymers, as well as random
walk in random environment, are covered. The restriction needed is on the
moment of the potential, in relation to the degree of mixing of the ergodic
environment. We derive two variational formulas for the limiting quenched free
energy and prove a process-level quenched large deviation principle for the
empirical measure. As a corollary we obtain LDPs for types of random walk in
random environment not covered by earlier results.
