  We study the asymptotic law of a network of interacting neurons when the
number of neurons becomes infinite. Given a completely connected network of
neurons in which the synaptic weights are Gaussian correlated random variables,
we describe the asymptotic law of the network when the number of neurons goes
to infinity. We introduce the process-level empirical measure of the
trajectories of the solutions to the equations of the finite network of neurons
and the averaged law (with respect to the synaptic weights) of the trajectories
of the solutions to the equations of the network of neurons. The main result of
this article is that the image law through the empirical measure satisfies a
large deviation principle with a good rate function which is shown to have a
unique global minimum. Our analysis of the rate function allows us also to
characterize the limit measure as the image of a stationary Gaussian measure
defined on a transformed set of trajectories.
