Quenched localisation in the Bouchaud trap model with slowly varying traps
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∈{2,3,…}N∈{2,3,…} there exists a slowly varying tail such that quenched localisation occurs on exa...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2016
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| _version_ | 1811140026177683456 |
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| author | Croydon, DA Muirhead, S |
| author_facet | Croydon, DA Muirhead, S |
| author_sort | Croydon, DA |
| collection | OXFORD |
| description | 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∈{2,3,…}N∈{2,3,…} 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. |
| first_indexed | 2024-03-06T23:02:03Z |
| format | Journal article |
| id | oxford-uuid:62782263-f958-43b0-b145-1e3cb62a726d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:15:26Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:62782263-f958-43b0-b145-1e3cb62a726d2024-07-17T09:21:21ZQuenched localisation in the Bouchaud trap model with slowly varying trapsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:62782263-f958-43b0-b145-1e3cb62a726dEnglishSymplectic Elements at OxfordSpringer2016Croydon, DAMuirhead, SWe 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∈{2,3,…}N∈{2,3,…} 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. |
| spellingShingle | Croydon, DA Muirhead, S Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title | Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title_full | Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title_fullStr | Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title_full_unstemmed | Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title_short | Quenched localisation in the Bouchaud trap model with slowly varying traps |
| title_sort | quenched localisation in the bouchaud trap model with slowly varying traps |
| work_keys_str_mv | AT croydonda quenchedlocalisationinthebouchaudtrapmodelwithslowlyvaryingtraps AT muirheads quenchedlocalisationinthebouchaudtrapmodelwithslowlyvaryingtraps |