  We consider a system of particles which interact through a jump process. The
jump intensities are functions of the proximity rank of the particles, a type
of interaction referred to as topological in the literature. Such interactions
have been shown relevant for the modelling of bird flocks. We show that, in the
large number of particles limit and under minimal smoothness assumptions on the
data, the model converges to a kinetic equation which was derived in earlier
works both formally and rigorously under more stringent regularity assumptions.
The proof relies on the coupling method which assigns to the particle and
limiting processes a joint process posed on the cartesian product of the two
configuration spaces of the former processes. By appropriate estimates in a
suitable Wasserstein metric, we show that the distance between the two
processes tends to zero as the number of particles tends to infinity, with an
error typical of the law of large numbers.
