2012/11/08 by D. Coupier, Coupier, D., Yu. I. Davydov +1
Mathematics · #52A22 #60D05 #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1211.1785
openalex publication_date 2012/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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√(n), with c>0, for Steiner.