The Annals of Applied Probability

Spectral characterization of aging: The REM-like trap model

Anton Bovier and Alessandra Faggionato

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Abstract

We review the aging phenomenon in the context of the simplest trap model, Bouchaud’s REM-like trap model, from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalized exactly. Using this result, we derive closed expressions for correlation functions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a “grand canonical” representation of the model in terms of the Markov process on a Poisson point process. In this context we analyze the dynamics on various time scales.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 3 (2005), 1997-2037.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1121433775

Digital Object Identifier
doi:10.1214/105051605000000359

Mathematical Reviews number (MathSciNet)
MR2152251

Zentralblatt MATH identifier
1086.60064

Subjects
Primary: 60K37: Processes in random environments 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

Keywords
Disordered systems random dynamics trap models aging spectral properties

Citation

Bovier, Anton; Faggionato, Alessandra. Spectral characterization of aging: The REM-like trap model. Ann. Appl. Probab. 15 (2005), no. 3, 1997--2037. doi:10.1214/105051605000000359. https://projecteuclid.org/euclid.aoap/1121433775


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