We consider a Vlasov-Fokker-Planck equation governing the evolution
of the density of interacting and diffusive matter in the space of
positions and velocities.
We use a probabilistic interpretation to obtain convergence towards
equilibrium in Wasserstein distance with an explicit exponential
rate. We also prove a propagation of chaos property for an
associated particle system, and give rates on the approximation of
the solution by the particle system. Finally, a transportation
inequality for the distribution of the particle system leads to
quantitative deviation bounds on the approximation of the
equilibrium solution of the equation by an empirical mean of the
particles at given time.