Asymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scales

Luiz Renato Fontes (1) , Véronique Gayrard (2)

1 IME-USP - Institute of Mathematics and Statistics [Sao Paulo]
2 I2M - Institut de Mathématiques de Marseille

We derive scaling limit results for the Random Hopping Dynamics for the cascading two-level GREM at low temperature at extreme time scales. It is known that in the cascading regime there are two static critical temperatures. We show that there exists a (narrow) set of fine tuning temperatures; when they lie below the static lowest critical temperature, three distinct dynamical phases emerge below the lowest critical temperature, with three different types of limiting dynamics depending on whether the temperature is (well) above or below, or at a fine tuning temperature, all of which are given in terms of K processes. We also derive scaling limit results for temperatures between the lowest and he highest critical ones, as well as aging results for all the limiting processes mentioned above, by taking a second small time limit.

Mots clés: GREM; Random Hopping Dynamics; low temperature; fine tuning temperature; scaling limit; extreme time-scale; K process; aging; spin glasses

Domaines: Mathématiques [math]; Probabilités [math.PR]

Luiz Renato Fontes, Véronique Gayrard. Asymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scales. Electronic Journal of Probability, In press. ⟨hal-02379027⟩