Random Symmetrizations of Convex Bodies. (September 2014)

• Record Type: Journal Article
• Authors: Coupier, D.; Davydov, Yu.
• Is Part Of: Advances in applied probability. Volume 46:Number 3(2014)
• Page Start: 603
• Page End: 621
• Publication Date: 2014-09
• Subjects: Stochastic geometry, -- convex geometry, -- limit shape, -- Steiner and Minkowski symmetrizations; 60D05, -- 52A22; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1409319551
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract : 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.