Abstract
We study the stability in finite times of the trajectories of interacting particles. Our aim isto show that on average and uniformly in the number of particles, two trajectories whoseinitial positions in phase space are close remain close enough at later times. For potentialsless singular than the classical electrostatic kernel, we are able to prove such a result forinitial positions/velocities distributed according to the Gibbs equilibrium of thesystem.
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