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We take the point of view of the particle in a multidimensional nearestneighbor random walk in random environment (RWRE). We prove a quenched largedeviation principle and derive a variational formula for the quenched ratefunction. Most of the previous results in this area rely on the subadditiveergodic theorem. We employ a different technique which is based on a minimaxtheorem. Large deviation principles for RWRE have been proven for i.i.d.nestling environments subject to a moment condition and for ergodic uniformlyelliptic environments. We assume only that the environment is ergodic and thetransition probabilities satisfy a moment condition.

Quenched large deviations for multidimensional random walk in random environment: a variational formula