Quenched localisation in the Bouchaud trap model with slowly varying traps
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Volume
168
Pagination
269 - 315
Publisher
Journal
Probability Theory and Related Fields
ISSN
0178-8051
Metadata
Show full item recordAbstract
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 $N \in \{2, 3, \ldots\}$ 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.
Authors
Croydon, D; Muirhead, SCollections
- Mathematics [1439]