Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 20 (2015), paper no. 25, 15 pp.
Two-site localisation in the Bouchaud trap model with slowly varying traps
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–>
Electron. Commun. Probab., Volume 20 (2015), paper no. 25, 15 pp.
Accepted: 13 March 2015
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
This work is licensed under a Creative Commons Attribution 3.0 License.
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