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Joint Applied Math and Probability Seminar
On some non-hierarchical generalizations of the random energy model
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Despite the recent remarkable progress in the understanding of the SK-model by Guerra and Talagrand, the ultrametricity is still not well understood. The random energy model (REM) and its generalization, the so called "generalized random energy model" (GREM), introduced by Derrida, had been crucial to get some understanding of spin glasses, but unfortunately, they don't shed any light on ultrametricity, simply because the models have an inbuilt ultrametric structure and therefore, there is nothing to understand regarding this question. We introduce some simple non-hierarchical generalizations of these models where asymptotic ultrametricity is a non-trivial question, which can be answered positively in some cases. |