The Annals of Probability

Scaling limit for trap models on ℤd

Gérard Ben Arous and Jiří Černý

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We give the “quenched” scaling limit of Bouchaud’s trap model in d≥2. This scaling limit is the fractional-kinetics process, that is the time change of a d-dimensional Brownian motion by the inverse of an independent α-stable subordinator.

Article information

Ann. Probab. Volume 35, Number 6 (2007), 2356-2384.

First available: 8 October 2007

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Mathematical Reviews number (MathSciNet)

Primary: 60K37: Processes in random environments 60G52: Stable processes 60F17: Functional limit theorems; invariance principles
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Trap model scaling limit Lévy process random walk fractional kinetics subordination


Ben Arous, Gérard; Černý, Jiří. Scaling limit for trap models on ℤ d . The Annals of Probability 35 (2007), no. 6, 2356--2384. doi:10.1214/009117907000000024.

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