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

We derive the scaling limit for the Hierarchical Random Hopping dynamics for the non cascading 2-GREM at low temperatures and time scales where the dynamics is close to equilibrium. The fine tuning phenomenon plays a role (under certain choices of parameters of the model), yielding three dynamical regimes. In contrast to the cascading case, the pairs of first and second level energies have fluctuations which scale with the volume, and this leads to a family of time scales where we see the dynamics moving through only a part of the full low-temperature energy landscape.

Automated summary

The scaling limit for the Hierarchical Random Hopping dynamics for the non cascading 2-GREM is derived in this study at low temperatures and time scales where the dynamics is close to equilibrium. The fine tuning phenomenon leads to three dynamical regimes depending on the choices of model parameters. In contrast to the cascading case, fluctuations in the pairs of first and second level energies scale with the volume, resulting in a range of time scales where the dynamics only moves through a portion of the full low-temperature energy landscape.