%0 Journal Article
%T Randomly trapped random walks on $\mathbb Z^d$
%A Ji£¿¨ª £¿erny
%A Tobias Wassmer
%J Mathematics
%D 2014
%I arXiv
%X We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. 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 $\mathbb Z^d$, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in [BCCR13].
%U http://arxiv.org/abs/1406.0363v4