  We study in this paper the effect of an unique initial stimulation on random
recurrent networks of leaky integrate and fire neurons. Indeed given a
stochastic connectivity this so-called spontaneous mode exhibits various non
trivial dynamics. This study brings forward a mathematical formalism that
allows us to examine the variability of the afterward dynamics according to the
parameters of the weight distribution. Provided independence hypothesis (e.g.
in the case of very large networks) we are able to compute the average number
of neurons that fire at a given time -- the spiking activity. In accordance
with numerical simulations, we prove that this spiking activity reaches a
steady-state, we characterize this steady-state and explore the transients.
