Title: Trap models at the ergodic scale.

Abstract:

In this talk we are going to discuss scaling limits of the so-called 'trap models', which first appeared as a simplification of spin-glass dynamics. To construct a trap model, we start with any give (continuous time) random walk and, in each state x of the chain, we add a trap with random depth W(x). The depth W(x) will multiply the time spent by the chain in the state x. If the depths of these random traps have a polynomial tail distribution, then the model typically presents an interesting aging behavior, which has been intensively studied. In this talk we are going to describe this system when it is let run for much longer (ergodic) times. For this we need to make use of the K-process introduced by Fontes and Mathieu. Moreover we develop a novel topology on the Skorohod space, which we believe to be useful in the analysis of metastability.