A quenched large deviation principle and a Parisi formula for a Perceptron version of the GREM
arXiv:1011.5686
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.
Dedicated to Juergen Gaertner on the occasion of his 60th birthday