Brazilian Journal of Probability and Statistics

Sub-Gaussian bound for the one-dimensional Bouchaud trap model

Manuel Cabezas

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Abstract

We establish a sub-Gaussian lower bound for the transition kernel of the one-dimensional, symmetric Bouchaud trap model, which provides a positive answer to the behavior predicted by Bertin and Bouchaud in (Phys. Rev. E (3) 67 (2013) 026128). The proof rests on the Ray–Knight description of the local time of a one-dimensional Brownian motion. Using the same ideas, we also prove the corresponding result for the FIN singular diffusion.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 1 (2015), 112-131.

Dates
First available in Project Euclid: 30 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1414674778

Digital Object Identifier
doi:10.1214/13-BJPS231

Mathematical Reviews number (MathSciNet)
MR3299110

Zentralblatt MATH identifier
1329.60355

Keywords
Bouchaud trap model FIN diffusion Ray–Knight Theorem

Citation

Cabezas, Manuel. Sub-Gaussian bound for the one-dimensional Bouchaud trap model. Braz. J. Probab. Stat. 29 (2015), no. 1, 112--131. doi:10.1214/13-BJPS231. https://projecteuclid.org/euclid.bjps/1414674778


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