The Annals of Probability

Scaling limit for trap models on ℤd

Gérard Ben Arous and Jiří Černý

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 8 October 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1191860424

Digital Object Identifier
doi:10.1214/009117907000000024

Zentralblatt MATH identifier
1134.60064

Mathematical Reviews number (MathSciNet)
MR2353391

Subjects
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)

Keywords
Trap model scaling limit Lévy process random walk fractional kinetics subordination

Citation

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. http://projecteuclid.org/euclid.aop/1191860424.


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References

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