A Quenched Large Deviation Principle and a Parisi Formula for a Perceptron Version of the GREM
We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov-type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation through a variational formula, which is closely related to the Parisi variational formula for the SK-model.
KeywordsFree Energy Relative Entropy Gibbs Measure Polish Space Variational Formula
E. Bolthausen is supported in part by the grant No 200020125247 ∕ 1 of the Swiss Science Foundation. N. Kistler is partially supported by the German Research Council in the SFB 611 and the Hausdorff Center for Mathematics.
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