Large Deviations, Guerra’s and A.S.S. Schemes, and the Parisi Hypothesis

Abstract

We investigate the problem of computing $$\lim_{N \to \infty}\frac{1}{aN}\log EZ_N^a$$ for any value of a, where Z N is the partition function of the celebrated Sherrington-Kirkpatrick (SK) model, or of some of its natural generalizations. This is a natural “large deviation” problem. Its study helps to get a fresh look at some of the recent ideas introduced in the area, and raises a number of natural questions. We provide a complete solution for a ≥ 0.