EXPECTED MEAN WIDTH OF THE RANDOMIZED INTEGER CONVEX HULL

Abstract

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.