Geodesic
Recent Results on Random Polytopes
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 17-39

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This is a survey over recent asymptotic results on random polytopes in d-dimensional Euclidean space. Three ways of generating a random polytope are considered: convex hulls of finitely many random points, projections of a fixed high-dimensional polytope into a random d-dimensional subspace, intersections of random closed halfspaces. The type of problems for which asymptotic results are described is different in each case. 
Schneider, Rolf. Recent Results on Random Polytopes. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 17-39. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a1/
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     title = {Recent {Results} on {Random} {Polytopes}},
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     url = {http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a1/}
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