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Randomly trapped random walks. (English) Zbl 1329.60354

Authors’ 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.

MSC:

60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G52 Stable stochastic processes
05C81 Random walks on graphs
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References:

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