A quenched large deviation principle and a Parisi formula for a Perceptron version of the GREM

2010/11/25 by E. Bolthausen, Bolthausen, E., N. Kistler +1
Computer Science · Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math.PR

paper · pdf · doi:10.48550/arxiv.1011.5686

Dedicated to Juergen Gaertner on the occasion of his 60th birthday

arxiv created 2010/11/25 · arxiv updated 2010/11/29

Abstract

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.

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