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15 06 IM ProbabilitySeminar noticiaTitulo: Asymptotic behavior of a low temperature non-cascading 2-GREM dynamics at extreme time scales

Palestrante: Leonel Zuaznábar (IME-USP)

Data: 20/06/2022
Horário: 15:00h às 16:00h (Rio de Janeiro local time)
Local: Transmissão online

Confira AQUI o link para a transmissão.

Resumo: We are interested in the study of a class of spin glass models introduced by Derrida under the name of Generalized Random Energy Models (GREM). They are based on Gaussian random variables on the hypercube {-1,1}^N with an inherent hierarchical correlation structure. More specifically, we consider the 2-GREM model evolving under the Random Hopping Dynamics at extreme time scales, where it is close to equilibrium, and visits the configurations in the support of the Gibbs measure. There are two scenarios that may be distinguished: the cascading case (studied by Luiz Renato Fontes and Veronique Gayrard in 2019) and the non-cascading case. The cascading occurs when the ground states energies are achieved by adding up the ground states energies of the two levels. In the non-cascading case the correlations are too weak to have an impact on the extremes and the system "collapses'' to a Random Energy Models (REM). Also, in this case, the extremal configurations must differ in the first index, this phenomenon justifies the non-cascading denomination for our system. In this work we got some results about the asymptotic behavior of the GREM model and the Random Hopping Dynamics in the non-cascading case.

Joint work with Luiz Renato Fontes and Susana Frómeta.

Organizadores: Giulio Iacobelli and Maria Eulalia Vares

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