  An analytical description of the response properties of simple but realistic
neuron models in the presence of noise is still lacking. We determine
completely up to the second order the firing statistics of a single and a pair
of leaky integrate-and-fire neurons (LIFs) receiving some common slowly
filtered white noise. In particular, the auto- and cross-correlation functions
of the output spike trains of pairs of cells are obtained from an improvement
of the adiabatic approximation introduced in \cite{Mor+04}. These two functions
define the firing variability and firing synchronization between neurons, and
are of much importance for understanding neuron communication.
