An almost sure central limit theorem for the overlap parameters in the Hopfield model

Gentz, B (1996). An almost sure central limit theorem for the overlap parameters in the Hopfield model. Stochastic Processes and their Applications, 62(2):243-262.

Abstract

We consider the Hopfield model with a finite number of randomly chosen patterns above and below the critical temperature and prove an almost sure conditional central limit theorem for the vector of overlap parameters. For this purpose we analyse the almost sure asymptotic behaviour of the partition function.

Abstract

We consider the Hopfield model with a finite number of randomly chosen patterns above and below the critical temperature and prove an almost sure conditional central limit theorem for the vector of overlap parameters. For this purpose we analyse the almost sure asymptotic behaviour of the partition function.

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