Transport Regimes in Random Walks in Random Environments

Hazel Brookfield; Wei Zhou; Ian Weatherby

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arXiv · 2601.06751

Transport Regimes in Random Walks in Random Environments

Hazel Brookfield·Wei Zhou·Ian Weatherby

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Abstract

Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies principal transport regimes through quantitative observables (velocity, diffusivity, mean-square displacement, first-passage, large deviations, aging), and reviews core methods in one dimension (potential/valley mechanisms) and in higher dimensions (environment-seen-from-the-particle, correctors/homogenization, regeneration and ballisticity criteria).

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Hazel Brookfield, Wei Zhou, Ian Weatherby. 2026-01-11. Transport Regimes in Random Walks in Random Environments. https://arxiv.org/abs/2601.06751

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