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The Hopfield Model on a Sparse Erdös-Renyi Graph

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Abstract

We analyze the storage capacity of the Hopfield model on a sparse G(N,p) random graph. We show that it is proportional to αpN in the entire regime where the corresponding random graph is asymptotically connected and for all value of α≤α c =0.03.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstraße 62, 48149, Münster, Germany

    Matthias Löwe

  2. Laboratoire de Mathématiques, UMR CNRS 6205, Université de Bretagne Occidentale, 6, avenue Victor Le Gorgeu, CS 93837, 29238, Brest Cedex 3, France

    Franck Vermet

Authors
  1. Matthias Löwe
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  2. Franck Vermet
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Correspondence to Franck Vermet.

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Löwe, M., Vermet, F. The Hopfield Model on a Sparse Erdös-Renyi Graph. J Stat Phys 143, 205–214 (2011). https://doi.org/10.1007/s10955-011-0167-1

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  • DOI: https://doi.org/10.1007/s10955-011-0167-1

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