Work

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

Year: 2026

Type: article

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.

Source: The Annals of Applied Probability

DOI: 10.1214/26-aap2325

Authors: Rangel Baldasso, Marcelo Hilário, Daniel Kious, Augusto Teixeira

Institutions: Pontifícia Universidade Católica do Rio de Janeiro, Universidade Federal de Minas Gerais, University of Bath, University of Lisbon

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Engineering and Physical Sciences Research Council

Award: G7746679952