Rigorous Solution of the Gardner Problem

نویسندگان

  • Mariya Shcherbina
  • Brunello Tirozzi
چکیده

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 p random patterns. The Gardner formula for this volume in the limit N, p→ ∞, p/N → α is proven for all values of α. Besides, we prove a useful criterion of the factorisation of all correlation functions for a class of spin glass model.

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تاریخ انتشار 2003