  The relative timing of action potentials in neurons recorded from local
cortical networks often shows a non-trivial dependence, which is then
quantified by cross-correlation functions. Theoretical models emphasize that
such spike train correlations are an inevitable consequence of two neurons
being part of the same network and sharing some synaptic input. For non-linear
neuron models, however, explicit correlation functions are difficult to compute
analytically, and perturbative methods work only for weak shared input. In
order to treat strong correlations, we suggest here an alternative
non-perturbative method. Specifically, we study the case of two leaky
integrate-and-fire neurons with strong shared input. Correlation functions
derived from simulated spike trains fit our theoretical predictions very
accurately. Using our method, we computed the non-linear correlation transfer
as well as correlation functions that are asymmetric due to inhomogeneous
intrinsic parameters or unequal input.
