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We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law…

In this paper the celebrated arcsine aging scheme of G. Ben Arous and J. Cern\'y is taken up. Using a brand new approach based on point processes and weak convergence techniques, this scheme is implemented in a wide class of Markov…

We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011),…

In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchaud's 'REM-like' trap model. We show that, below the critical temperature, if we consider a…

We review the ageing phenomenon in the context of 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 diagonalised exactly. Using this…

We study the aging behavior of the Random Energy Model (REM) evolving under Metropolis dynamics. We prove that a classical two-time correlation function converges almost surely to the arcsine law distribution function that characterizes…

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…

The GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume $L$-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural…

We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We…

In this paper, we prove that if a sequence of electrical networks converges in the local Gromov-Hausdorff topology and satisfies a non-explosion condition, then the associated Bouchaud trap models (BTMs) also converge and exhibit aging.…

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the…

We consider Random Hopping Time (RHT) dynamics of the Sherrington - Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature we prove that, on time scales that are sub-exponential in…

We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy…

Applying the new tools developed in [G1], we investigate the arcsine aging regime of the random hopping time dynamics of the REM. Our results are optimal in several ways. They cover the full time-scale and temperature domain where this…

Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a…

Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…

We prove non-convergence theorems towards an unstable equilibrium (or a trap) for stochastic processes. The processes we consider are continuous-time or discrete-time processes and can be pertubations of the flow generated by a vector…

We obtain scaling limit results for asymmetric trap models and their infinite volume counterparts, namely asymmetric K processes. Aging results for the latter processes are derived therefrom.

We consider one-dimensional directed trap models and suppose that the trapping times are heavy-tailed. We obtain the inverse of a stable subordinator as scaling limit and prove an aging phenomenon expressed in terms of the generalized…

We consider trap models on Z^d, namely continuous time Markov jump process on Z^d with embedded chain given by a generic discrete time random walk, and whose mean waiting time at x is given by tau_x, with tau = (tau_x, x in Z^d) a family of…