Central limit theorems for Gaussian polytopes
By Imre Bárány, Van H. Vu. 2006
145 citations recorded by the source corpus.
Choose n random, independent points in R d according to the standard normal distribution. Their convex hull K n is the Gaussian random polytope. We prove that the volume and the number of faces of K n satisfy the central limit theorem, settling a well-known conjecture in the field.
Subfields: Applied Mathematics, Food Science, Forestry
View Paper: https://www.semanticscholar.org/paper/8af8d6f10bc5688a3e0561b76b0caadd60e2bba0
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In Applied Mathematics
- Zakhar Kabluchko
- C. Thaele
- Daniel Temesvari
- Imre Bárány
- Matthias Schulte
- Günter Last
- Giovanni Peccati
In Food Science
In Forestry
Citations in the corpus
- Expected intrinsic volumes and facet numbers of random beta‐polytopes (2017, methodology): “For selected examples we refer to the works of Bárány, Fodor and Vigh [6], Bárány and Vu [8] and Reitzner [30,31], and to the survey articles of Bárány [5], Hug [20], Reitzner [32] and Schneider [34] as well as the references cited therein.”
- Random points and lattice points in convex bodies (2008, background): “This can be done by the following transference lemma from [25], which has been used in an implicit form in [51] and in [68], and perhaps elsewhere as well.”