The Annals of Applied Probability

Spectral characterization of aging: The REM-like trap model

Anton Bovier and Alessandra Faggionato

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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.

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

First available in Project Euclid: 15 July 2005

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

Disordered systems random dynamics trap models aging spectral properties


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.

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