  In this paper we prove the propagation of chaos property for an ensemble of
interacting neurons subject to independent Brownian noise. The propagation of
chaos property means that in the large network size limit, the neurons behave
as if they are probabilistically independent. The model for the internal
dynamics of the neurons is taken to be that of Wilson and Cowan, and we
consider there to be multiple different populations. The synaptic connections
are modelled with a nonlinear `electrical' model. The nonlinearity of the
synaptic connections means that our model lies outside the scope of classical
propagation of chaos results. We obtain the propagation of chaos result by
taking advantage of the fact that the mean-field equations are Gaussian, which
allows us to use Borell's Inequality to prove that its tails decay
exponentially.
