Rigorous Solution of the Gardner Problem

Details Rigorous Solution of the Gardner Problem Rigorous Solution of the Gardner Problem

2001-12-03

arxiv.org/abs/math-ph/0112003v1

Physics

Mathematical Physics

38 pages

Scientific paper

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 \alpha is proven for all values of \alpha. Besides, we prove a useful criterion of the factorisation of all the correlation functions for a class of spin glass model.

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