Metastability in the generalized Hopfield model with finitely many patterns

Authors
Type
Preprint
Publication Date
Apr 26, 2009
Submission Date
Mar 17, 2009
Identifiers
arXiv ID: 0903.3050
Source
arXiv
License
Yellow
External links

Abstract

This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns $\xi_1,...,\xi_p$ where the patterns have i.i.d. components and follow discrete distributions on $[-1,1]$. We show that metastable behaviour occurs and provide sharp asymptotics on metastable exit times and the corresponding capacities. We apply the potential theoretic approach developed by Bovier et al. in the space of appropriate order parameters and use an analysis of the discrete Laplacian to obtain lower bounds on capacities. Moreover, we include the possibility of multiple saddle points with the same value of the rate function and the case that the energy surface is degenerate around critical points.

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