Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh

2023/04/12 by Rangel Baldasso, Marcelo R. Hilário, Baldasso, Rangel +5 · 1 citation
Mathematics · #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2304.05771

openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove a lower bound for the fluctuations of symmetric random walks on dynamic random environments in dimension 1 + 1 in the perturbative regime where the walker is weakly influenced by the environment. We suppose that the random environment is invariant with respect to translations and reflections, satisfies the FKG inequality and a mild mixing condition. The techniques employed are inspired by percolation theory, including a Russo-Seymour-Welsh (RSW) inequality. To exemplify the generality of our results, we provide two families of fields that satisfy our hypotheses: a class of Gaussian fields and Confetti percolation models.

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