Published online by Cambridge University Press: 01 July 2016
An exact expression is determined for the asymptotic constant c2 in the limit theorem by P. Groeneboom (1988), which states that the number of vertices of the convex hull of a uniform sample of n random points from a circular disk satisfies a central limit theorem, as n → ∞, with asymptotic variance 2πc2n1/3.
Partially supported by a Clay Book Fellowship.
Partially supported by PSC-CUNY grant no. 60032-33-34.