# Randomly trapped random walks on $\\mathbb Z^d$

Source: [Randomly trapped random walks on $\\mathbb Z^d$](<https://www.sota2.com/research/paper/68fa51291e209131ce9717f9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T04:56:50.462Z

Authors: Ji\\v{r}\\'i \\v{C}ern\\'y, Tobias Wassmer

Published: 2014-06-02T13:35:49.000Z

## Abstract

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 \[BCCR13\].

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1406.0363>)

[PDF](<https://arxiv.org/pdf/1406.0363.pdf>)