2005/07/15 by Anton Bovier, Alessandra Faggionato
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Theoretical and Computational Physics #math.PR #msc:60K37 #msc:82C20 #stochastic dynamics and bifurcation
paper · pdf · doi:10.1214/105051605000000359
published as Annals of Applied Probability 2005, Vol. 15, No. 3, 1997-2037 · 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)
openalex publication_date 2005/07/15 · arxiv created 2005/08/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.