Spectral characterization of aging: The REM-like trap model

Anton Bovier, Alessandra Faggionato
2005 The Annals of Applied Probability  
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
more » ... l in terms of the Markov process on a Poisson point process. In this context we analyze the dynamics on various time scales.
doi:10.1214/105051605000000359 fatcat:wxyktzhu6bgx5cgfplz3skdejm