  We prove a quantitative result of convergence of a conservative stochastic
particle system to the solution of the homogeneous Landau equation for hard
potentials. There are two main difficulties: (i) the known stability results
for this class of Landau equations concern regular solutions and seem difficult
to extend to study the rate of convergence of some empirical measures; (ii) the
conservativeness of the particle system is an obstacle for (approximate)
independence. To overcome (i), we prove a new stability result for the Landau
equation for hard potentials concerning very general measure solutions. Due to
(ii), we have to couple, our particle system with some non independent
nonlinear processes, of which the law solves, in some sense, the Landau
equation. We then prove that these nonlinear processes are not so far from
being independent. Using finally some ideas of Rousset [25], we show that in
the case of Maxwell molecules, the convergence of the particle system is
uniform in time.
