Abstract
While the derivations of precise asymptotic estimates found in the mathematical literature are not easily accessible to the non-specialist, there are rather simple arguments for deriving rougher "big-theta" bounds on the expected size of random convex hulls. These arguments are presented, then applied to verify a recently published conjecture on the expected number of maximal vectors among a set of random points chosen from a ball. A summary of recent progress follows. Results relevant for analyzing algorithms are emphasized.
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