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

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

2010-11-25

arxiv.org/abs/1011.5686v1

Mathematics

Probability

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

Scientific paper

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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