2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116678We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis of \cite{Zer}, where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting.Probability60K37text