Work

Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions

Year: 2025

Type: article

Abstract: We consider a random walk in a random environment on Zd under ballisticity condition (T). We show the existence of the invariant measure Q with respect to the environment viewed from the particle for d=2 and d=3, which disproves a conjecture made in [3] regarding the two-dimensional case. We also prove tail estimates for the Radon-Nikodym derivative dQ∕dP, where P is the original distribution on the environment. Lastly, we provide nearly sharp tail bounds for regeneration times for d=3.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1377

Author: Tal Peretz

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Israel Science Foundation, Technion-Israel Institute of Technology