Let X1,…,Xn be independent random points that are distributed according to a probability measure on Rd and let Pn be the random convex hull generated by X1,…,Xn (n≥d+1). For natural classes of probability distributions and by means of Blaschke–Petkantschin formulae from integral geometry it is shown that the mean facet number of Pn is strictly monotonically increasing in n.
Bonnet, G., Grote, J., Temesvari, D., Thale, C., Turchi, N., Wespi, F. (2017). Monotonicity of facet numbers of random convex hulls. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 455(2), 1351-1364 [10.1016/j.jmaa.2017.06.054].
Monotonicity of facet numbers of random convex hulls
Turchi N.
;
2017
Abstract
Let X1,…,Xn be independent random points that are distributed according to a probability measure on Rd and let Pn be the random convex hull generated by X1,…,Xn (n≥d+1). For natural classes of probability distributions and by means of Blaschke–Petkantschin formulae from integral geometry it is shown that the mean facet number of Pn is strictly monotonically increasing in n.
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