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

2025/06/02 by Jiaming Chen, Chen, Jiaming
Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2506.01316

openalex publication_date 2025/06/02 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Velocity surface disorder of large deviation rate functions of the random walk in strongly mixing environment
• Selected Topics in Random Walk in Random Environment
• Quenched Point-to-Point Free Energy for Random Walks in Random Potentials

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