Geodesic
Gale Duality and the Neighborliness of Random Polytopes. II
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 4, pp. 87-109

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We have obtain of some distribution-independent results on the $k$-neighborliness of random polytopes. They confirm the well-known Gale conjecture for the general case.
Keywords: $k$-neighborly polytope, probability space, random points, random polytope, distribution-independent property. 
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     author = {A. G. Brodskiy},
     title = {Gale {Duality} and the {Neighborliness} of {Random} {Polytopes.} {II}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {87--109},
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     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_4_a8/}
}
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A. G. Brodskiy. Gale Duality and the Neighborliness of Random Polytopes. II. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 4, pp. 87-109. http://geodesic.mathdoc.fr/item/MAIS_2012_19_4_a8/