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

E. Bolthausen; N. Kistler

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

Probability 2010-11-29 v1

Authors: E. Bolthausen , N. Kistler

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.

Keywords

generalized random energy model perceptron quenched large deviation principle sanov theorem parisi formula sk-model

Cite

@article{arxiv.1011.5686,
  title  = {A quenched large deviation principle and a Parisi formula for a Perceptron version of the GREM},
  author = {E. Bolthausen and N. Kistler},
  journal= {arXiv preprint arXiv:1011.5686},
  year   = {2010}
}

Comments

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

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