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We develop an analytic framework to investigate the stability of splay states in infinite networks of identical integrate-and-fire neurons coupled through synaptic pulses. More specifically we perform a linear stability analysis of the splay state probability distribution whose dynamics is governed by an appropriate Fokker Planck equation. For exponentially decaying synaptic pulses the splay state is unstable for excitation and stable for inhibition. For excitatory alpha-function pulses thedoi:10.1186/1471-2202-15-s1-p91 pmcid:PMC4126587 fatcat:eb2vg3bavvhl5kqwuw5nhafz7y