  We study the stability in finite times of the trajectories of interacting
particles. Our aim is to show that in average and uniformly in the number of
particles, two trajectories whose initial positions in phase space are close,
remain close enough at later times. For potential less singular than the
classical electrostatic kernel, we are able to prove such a result, for initial
positions/velocities distributed according to the Gibbs equilibrium of the
system.
