On a nonhierarchical generalization of the Perceptron GREM

2021/06/14 by Nicola Kistler, Kistler, Nicola, Giulia Sebastiani +1
Mathematics · #60G70 #60J80 #82B44 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G70 #msc:60J80 #msc:82B44

paper · pdf · doi:10.48550/arxiv.2106.07279

arxiv created 2021/06/14 · arxiv updated 2021/06/15

Abstract

We introduce a nonlinear, nonhierarchical generalization of Derrida's GREM and establish through a Sanov-type large deviation analysis both a Boltzmann-Gibbs principle as well as a Parisi formula for the limiting free energy. In line with the predictions of the Parisi theory, the free energy is given by the minimal value over all Parisi functionals/hierarchical structures in which the original model can be coarse-grained.

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