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2015 Two-site localisation in the Bouchaud trap model with slowly varying traps
Stephen Muirhead
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Electron. Commun. Probab. 20: 1-15 (2015). DOI: 10.1214/ECP.v20-3723

Abstract

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a stronger form of localisation than has previously been established in the literature for the Bouchaud trap model on the integers in the case of regularly varying traps. Underlying this result is the fact that the sum of a sequence of i.i.d. random variables with a slowly varying tail is asymptotically dominated by the maximal term.<!–EndFragment–>

Citation

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Stephen Muirhead. "Two-site localisation in the Bouchaud trap model with slowly varying traps." Electron. Commun. Probab. 20 1 - 15, 2015. https://doi.org/10.1214/ECP.v20-3723

Information

Accepted: 13 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60197
MathSciNet: MR3327864
Digital Object Identifier: 10.1214/ECP.v20-3723

Subjects:
Primary: 60H25
Secondary: 35P05, 60F10, 82C44

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