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

Understand

We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE).

• We prove a quenched large deviation principle and derive a variational formula for the quenched rate function.
• Most of the previous results in this area rely on the subadditive ergodic theorem.
• We employ a different technique which is based on a minimax theorem.