The Annals of Probability

Randomly trapped random walks

Gérard Ben Arous, Manuel Cabezas, Jiří Černý, and Roman Royfman

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We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb{Z}$. These scaling limits include the well-known fractional kinetics process, the Fontes–Isopi–Newman singular diffusion as well as a new broad class we call spatially subordinated Brownian motions. We give sufficient conditions for convergence and illustrate these on two important examples.

Article information

Ann. Probab., Volume 43, Number 5 (2015), 2405-2457.

Received: March 2013
Revised: February 2014
First available in Project Euclid: 9 September 2015

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments 60G52: Stable processes
Secondary: 60F17: Functional limit theorems; invariance principles

Bouchaud trap model random walk scaling limit percolation


Ben Arous, Gérard; Cabezas, Manuel; Černý, Jiří; Royfman, Roman. Randomly trapped random walks. Ann. Probab. 43 (2015), no. 5, 2405--2457. doi:10.1214/14-AOP939.

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