We study collective synchronization of pulse-coupled oscillators interacting
on asymmetric random networks. We demonstrate that random matrix theory can be
used to accurately predict the speed of synchronization in such networks in
dependence on the dynamical and network parameters. Furthermore, we show that
the speed of synchronization is limited by the network connectivity and stays
finite, even if the coupling strength becomes infinite. In addition, our
results indicate that synchrony is robust under structural perturbations of the
network dynamics.Comment: 5 pages, 3 figure