Rigorous Solution of the Gardner Problem

Abstract

We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of random patterns. The Gardner formula for this volume in the limit N,p \to \infty, p/N \to αis proven for all values of α. Besides, we prove a useful criterion of the factorisation of all the correlation functions for a class of spin glass model.

38 pages