In trying to understand the dynamics of the densely-connected neural networks that comprise the neocortex, a suitable first step is to study the firing statistics of neurons in a simple model of an isolated cortical column: a random network of a few thousand neurons, with any two of them connected with a probability of about 10%.
These neurons fire irregularly, at low rates, and these properties have been thought to be understood, for about a decade now, in terms of a self-consistent balance of excitation and inhibition. However, the existing theory requires correlations between neurons to be very small, in apparent disagreement with the experimentally observed degree of correlation. I will present some results of simulations of such models and some new theoretical ideas for a self-consistent treatment of correlations.