Abstract
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.
Funding Statement
LRF was partially supported by CNPq grants 311257/2014-3 and 307884/2019-8; and FAPESP grant 2017/10555-0. SF was partially supported by FAPESP grant 2017/10555-0 during visits to USP to carry out this research. LZ was supported by a PNPD/CAPES grant 88882.315481/2013-01 post doctoral fellowship.
Acknowledgements
We thank an anonymous referee for many specific comments to an earlier version of this text that much helped improve the presentation.
Citation
Luiz Renato Fontes. Susana Frómeta. Leonel Zuaznábar. "Asymptotic behavior of a low-temperature non-cascading 2-GREM dynamics at extreme time scales." Bernoulli 28 (4) 2716 - 2743, November 2022. https://doi.org/10.3150/21-BEJ1435
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