Scaling limit for trap models on ℤd

Gérard Ben Arous; Jiří Černý

doi:10.1214/009117907000000024

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Home > Journals > Ann. Probab. > Volume 35 > Issue 6 > Article

November 2007 Scaling limit for trap models on ℤ^d

Gérard Ben Arous, Jiří Černý

Ann. Probab. 35(6): 2356-2384 (November 2007). DOI: 10.1214/009117907000000024

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Abstract

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.

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Gérard Ben Arous. Jiří Černý. "Scaling limit for trap models on ℤ^d." Ann. Probab. 35 (6) 2356 - 2384, November 2007. https://doi.org/10.1214/009117907000000024