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Random Symmetrizations of Convex Bodies

Part of: Geometric probability and stochastic geometry General convexity

Published online by Cambridge University Press:  22 February 2016

D. Coupier  and
Yu. Davydov
D. Coupier*
Affiliation:
Université Lille 1
Yu. Davydov*
Affiliation:
Université Lille 1
*
∗ Postal address: Laboratoire Paul Painlevé, UMR CNRS 8524, Université Lille 1, 59 655 Villeneuve d'Ascq Cédex, France.
∗∗ Email address: [email protected]
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Abstract

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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.

Keywords

Stochastic geometryconvex geometrylimit shapeSteiner and Minkowski symmetrizations

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 603 - 621
Copyright
© Applied Probability Trust 

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