Rigorous Solution of the Gardner Problem

M. Shcherbina; B. Tirozzi

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arXiv · math-ph/0112003

Rigorous Solution of the Gardner Problem

M. Shcherbina·B. Tirozzi

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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.

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M. Shcherbina, B. Tirozzi. 2001-12-03. Rigorous Solution of the Gardner Problem. https://arxiv.org/abs/math-ph/0112003

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