Spike-count Distribution in a Neuronal Population Under Weak Common Stimulation

We study the probability distribution of the number of synchronous action potentials (spike count) in a model network consisting of a homogeneous neural population that is driven by a common time-dependent stimulus. We derive two analytical approximations for the count statistics, which are based on linear response theory and hold true for weak input correlations. Comparison to numerical simulations of populations of integrate-and-fire neurons in different parameter regimes reveals that our theory correctly predicts how much a weak common stimulus increases the probability of common firing and of common silence in the neural population.