On the asymptotic distribution of the area outside a random convex hull in a disk /

The asymptotic distribution of the area $V_n$ outside the convex hull of $n$ i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of $V_n$ is found to be of the order $n^{-5/3}$ and the asymptotic distribution of $V_n$ is shown to be normal. The re...

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