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

Quenched Free Energy and Large Deviations for Random Walks in Random Potentials