Electronic Communications in Probability

Two-site localisation in the Bouchaud trap model with slowly varying traps

Stephen Muirhead

Full-text: Open access

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–>

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 25, 15 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320952

Digital Object Identifier
doi:10.1214/ECP.v20-3723

Mathematical Reviews number (MathSciNet)
MR3327864

Zentralblatt MATH identifier
1327.60197

Subjects
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 82C44: Dynamics of disordered systems (random Ising systems, etc.) 60F10: Large deviations 35P05: General topics in linear spectral theory

Keywords
Bouchaud trap model localisation slowly varying tail

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Muirhead, Stephen. Two-site localisation in the Bouchaud trap model with slowly varying traps. Electron. Commun. Probab. 20 (2015), paper no. 25, 15 pp. doi:10.1214/ECP.v20-3723. https://projecteuclid.org/euclid.ecp/1465320952


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