  We develop and study a statistical test to detect synchrony in spike trains.
Our test is based on the number of coincidences between two trains of spikes.
The data are supplied in the form of \(n\) pairs (assumed to be independent) of
spike trains. The aim is to assess whether the two trains in a pair are also
independent. Our approach is based on previous results of Albert et al. (2015,
2019) and Kim et al. (2022) that we extend to our setting, focusing on the
construction of a non-asymptotic criterion ensuring the detection of
synchronization in the framework of permutation tests. Our criterion is
constructed such that it ensures the control of the Type II error, while the
Type I error is controlled by construction. We illustrate our results within
two classical models of interacting neurons, the jittering Poisson model and
Hawkes processes having \(M\) components interacting in a mean field frame and
evolving in stationary regime. For this latter model, we obtain a lower bound
of the size \(n\) of the sample necessary to detect the dependency between two
neurons.
