  We investigate the long-term relaxation of one-dimensional (${1D}$)
self-gravitating systems, using both kinetic theory and $N$-body simulations.
We consider thermal and Plummer equilibria, with and without collective
effects. All combinations are found to be in clear agreement with respect to
the Balescu-Lenard and Landau predictions for the diffusion coefficients.
Interestingly, collective effects reduce the diffusion by a factor ${\sim 10}$.
The predicted flux for Plummer equilibrium matches the measured one, which is a
remarkable validation of kinetic theory. We also report on a situation of quasi
kinetic blocking for the same equilibrium.
