 912 Koch H.
 A Scaling Limit of the Glauber Dynamics for a Class of Neural Network Models.
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Jul 10, 91

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Abstract. We consider the time evolution of d mean field variables for
networks of N neurons whose connection matrices J_N have d distinct rows.
Certain assumptions are made about the large N behavior of J_N,
which guarantee the convergence of a free energy density function.
These assumptions are known to be satisfied e.g. in the Hopfield model
with p stored patterns, for d=2^p. It is proved that in a scaling limit,
where N tends to infinity and d stays fixed, the time evolution approaches
that of a diffusion process in R^d. This process describes in detail,
and for times up to o(N^(3/2)) iterations, the dynamics of the
mean field fluctuations near a local minimum of the free energy density.
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