The randomised integer convex hull

by Imre Barany (Budapest and London)

Abstract. Assume $K \subset R^d$ is a convex body. Its randomised integer
convex hull is $I_L(K)= conv (K \cap L$, where $L$ is a randomly
translated and rotated copy of the integer lattice $Z^d$. Motivated by
integer programming, we estimate the expected number of vertices of
$I_L(K)$, and also the expected missed volume, that is, the
expectation of $Vol(K \setminus I_L(K))$. The outcome is similar, but
not identical, with the case of random polytopes. This is joint work with
J. Matousek.