Randomly trapped random walks on [formula omitted

Abstract

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on Zd, d≥2. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of its clock process is either deterministic linearly growing or a stable subordinator. In the case when the discrete skeleton is a simple random walk on Zd, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in Ben Arous et al. (2014).