Spectral characterization of aging: the rem-like trap model
arXiv:math/0508486 · doi:10.1214/105051605000000359
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.
Published at http://dx.doi.org/10.1214/105051605000000359 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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