Non-conformality of large deviations of moving average of the random walk in strongly mixing environment

Abstract

The quenched and annealed large deviations of the random walk in random environment are shown to conform on any compact set whenever the level of disorder is sufficiently low. In this work, we show that these two large deviations always disagree at some interior point of the natural domain of the random walk in strongly mixing environment, regardless of the level of disorder.