Randomly trapped random walks

Abstract

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.

Published at http://dx.doi.org/10.1214/14-AOP939 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Bouchaud's model exhibits two different aging regimes in dimension one
• Spectral characterization of aging: the rem-like trap model
• Invasion percolation on regular trees
• Scaling limit of the random walk among random traps on Z^d

Cited by in corpus (6)

• From Quenched Disorder to Continuous Time Random Walk
• The case of the biased quenched trap model in two dimensions with diverging mean dwell times
• The Transient Case of The Quenched Trap Model
• Non-Gaussian fluctuations of randomly trapped random walks
• Biased Random Walk on Spanning Trees of the Ladder Graph
• Aging and sub-aging for Bouchaud trap models on resistance metric spaces