EXPECTED MEAN WIDTH OF THE RANDOMIZED INTEGER CONVEX HULL

Autor(en): Ngoc, Binh Hong
Reitzner, Matthias 
Stichwörter: 52A20 (primary); 52A27 (secondary); 60C05; Mathematics; Mathematics, Applied
Erscheinungsdatum: 2021
Herausgeber: WILEY
Journal: MATHEMATIKA
Volumen: 67
Ausgabe: 2
Startseite: 422
Seitenende: 433
Zusammenfassung: 
Let K subset of Rd be a convex body, and assume that L is a randomly rotated and shifted integer lattice. Let KL be the convex hull of the (random) points K boolean AND L. The mean width W(KL) of KL is investigated. The asymptotic order of the mean width difference W(lambda K)-W((lambda K)L) is maximized by the order obtained by polytopes and minimized by the order for smooth convex sets as lambda ->infinity.
ISSN: 00255793
DOI: 10.1112/mtk.12080

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