  The stability of dynamical states characterized by a uniform firing rate
({\it splay states}) is analyzed in a network of $N$ globally pulse-coupled
rotators (neurons) subject to a generic velocity field. In particular, we
analyse short-wavelength modes that were known to be marginally stable in the
infinite $N$ limit and show that the corresponding Floquet exponent scale as
$1/N^2$. Moreover, we find that the sign, and thereby the stability, of this
spectral component is determined by the sign of the average derivative of the
velocity field. For leaky-integrate-and-fire neurons, an analytic expression
for the whole spectrum is obtained. In the intermediate case of continuous
velocity fields, the Floquet exponents scale faster than $1/N^2$ (namely, as
$1/N^4$) and we even find strictly neutral directions in a wider class than the
sinusoidal velocity fields considered by Watanabe and Strogatz in {\it Physica
D 74 (1994) 197-253}.

Disordered Systems and Neural Networks;Chaotic Dynamics;Neurons and Cognition