The Annals of Applied Probability· 2026Q1
Fluctuation bounds for symmetric random walks on dynamic environments via Russo–Seymour–Welsh
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- Q1SCImago
- 2026year
Short summary
A new lower bound for fluctuations of symmetric random walks in dynamic random environments (1+1D, perturbative regime) is proven using Russo-Seymour-Welsh techniques.
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Key points
- A lower bound for fluctuations of symmetric random walks in dynamic random environments (1+1D, perturbative regime) is proven.
- The proof utilizes Russo-Seymour-Welsh (RSW) inequality and percolation theory inspired techniques.
- Assumptions on the environment include translational/reflective invariance, FKG inequality, and a mild mixing condition.
- The results are exemplified by Gaussian fields and confetti percolation models.
AI-generated from the title and abstract; the full text is not read.
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, satisfy 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.
The authors' abstract, as published at the source. The Annals of Applied Probability, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics