Transport Regimes in Random Walks in Random Environments

TL;DR

This paper reviews transport behaviors in random walks within disordered environments, analyzing different regimes through various observables and core methods across dimensions.

Contribution

It provides a comprehensive summary of discrete and continuous models, identifying principal transport regimes and core analytical methods in one and higher dimensions.

Findings

Identification of key transport regimes via observables

Summary of core analytical methods in different dimensions

Comparison of discrete and continuous time formulations

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).