Randomly trapped random walks on \mathbb Z^d

2014/06/02 by Jiří Černý, Černý, Jiří, Tobias Wassmer +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1406.0363

revised version, 24 pages

arxiv created 2014/10/01 · arxiv updated 2014/10/02

Abstract

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on \mathbb Z^d, 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 \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].

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