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- W2334925741 abstract "It is well known that the vertices of the convex hull of n random points, which are chosen independently and uniformly from the interior of a convex polygon, are concentrated in the neighbourhoods of the vertices of the polygon as n tends to infinity. Here concentration means that the number of vertices of the convex hull outside of the neighbourhoods of the vertices of the polygon is negligible asymptotically. The first moment of the number of vertices of the convex hull in a neighbourhood of a vertex of the polygon was obtained in 1963 by Renyi and Sulanke in a classical paper. The second moment was achieved in 1988 by Groeneboom using a Poisson point process approximation technique. Due to the complexity of the occurring calculations the extension of this technique to higher moments appears to be out of reach. Based on a purely geometric approach, which avoids stochastic processes, we derive the moments of all orders." @default.
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- W2334925741 date "2012-03-01" @default.
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- W2334925741 title "On the boundary structure of the convex hull of random points" @default.
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- W2334925741 doi "https://doi.org/10.1515/advgeom.2011.041" @default.
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