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- W3179700993 abstract "Abstract For , let S be a set of points in in general position. A set I of k points from S is a k ‐ island in S if the convex hull of I satisfies . A k ‐island in S in convex position is a k ‐ hole in S . For and a convex body of volume 1, let S be a set of n points chosen uniformly and independently at random from K . We show that the expected number of k ‐holes in S is in . Our estimate improves and generalizes all previous bounds. In particular, we estimate the expected number of empty simplices in S by . This is tight in the plane up to a lower‐order term. Our method gives an asymptotically tight upper bound even in the much more general setting, where we estimate the expected number of k ‐islands in S ." @default.
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- W3179700993 date "2021-07-12" @default.
- W3179700993 modified "2023-09-30" @default.
- W3179700993 title "Holes and islands in random point sets" @default.
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- W3179700993 doi "https://doi.org/10.1002/rsa.21037" @default.
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