  In this paper, the asymptotic behavior of sequences of successive Steiner and
Minkowski symmetrizations is investigated. We state an equivalence result
between the convergences of those sequences for Minkowski and Steiner.
Moreover, in the case of independent (and not necessarily identically
distributed) directions, we prove the almost sure convergence of successive
symmetrizations at rate exponential for Minkowski, and at rate
$e^{-c\sqrt{n}}$, with $c>0$, for Steiner.
