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