01-443 Masha Shcherbina, Brunello Tirozzi
Rigorous Solution to the Gardner Problem (609K, Postscript) Dec 3, 01
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Abstract. We prove rigorrously 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 p 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 models.

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