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Functional limit theorems for the Bouchaud trap model with slowly-varying traps
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Croydon, David A. and Muirhead, Stephen (2015) Functional limit theorems for the Bouchaud trap model with slowly-varying traps. Stochastic Processes and their Applications, 125 (5). pp. 1980-2009. doi:10.1016/j.spa.2014.12.004 ISSN 0304-4149.
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Official URL: http://dx.doi.org/10.1016/j.spa.2014.12.004
Abstract
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly-varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the functional limit theorems previously established in the literature in the case of integrable or regularly-varying trap distribution. Reflecting the fact that the clock process is dominated in the limit by the contribution from the deepest-visited trap, the limit process for the model is a spatially-subordinated Brownian motion whose associated clock process is an extremal process. We identify this process as the α→0 scaling limit of the FIN diffusion with parameter α. Additionally, we study a natural `transparent' generalisation of the Bouchaud trap model with slowly-varying trap distribution.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
Publisher: | Elsevier Science BV | ||||||||
ISSN: | 0304-4149 | ||||||||
Official Date: | May 2015 | ||||||||
Dates: |
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Volume: | 125 | ||||||||
Number: | 5 | ||||||||
Page Range: | pp. 1980-2009 | ||||||||
DOI: | 10.1016/j.spa.2014.12.004 | ||||||||
Status: | Not Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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