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Quenched localisation in the Bouchaud trap model with slowly varying traps
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Croydon, David A. and Muirhead, Stephen (2017) Quenched localisation in the Bouchaud trap model with slowly varying traps. Probability Theory and Related Fields, 168 (1-2). pp. 269-315. doi:10.1007/s00440-016-0710-8 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-016-0710-8
Abstract
We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each Nā{2,3,ā¦} there exists a slowly varying tail such that quenched localisation occurs on exactly N sites. As far as we are aware, this is the first example of a model in which the exact number of localisation sites are able to be `tuned' according to the model parameters. Key intuition for this result is provided by an observation about the sum-max ratio for sequences of independent and identically distributed random variables with a slowly varying distributional tail, which is of independent interest.
Item Type: | Journal Article | ||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||||||||
Publisher: | Springer | ||||||||||
ISSN: | 0178-8051 | ||||||||||
Official Date: | June 2017 | ||||||||||
Dates: |
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Volume: | 168 | ||||||||||
Number: | 1-2 | ||||||||||
Page Range: | pp. 269-315 | ||||||||||
DOI: | 10.1007/s00440-016-0710-8 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access |
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