  Can Spiking Neural Networks (SNNs) approximate the dynamics of Recurrent
Neural Networks (RNNs)? Arguments in classical mean-field theory based on laws
of large numbers provide a positive answer when each neuron in the network has
many "duplicates", i.e. other neurons with almost perfectly correlated inputs.
Using a disordered network model that guarantees the absence of duplicates, we
show that duplicate-free SNNs can converge to RNNs, thanks to the concentration
of measure phenomenon. This result reveals a general mechanism underlying the
emergence of rate-based dynamics in large SNNs.
