Editing Central limit theorem (section)

===Gaussian polytopes===
{{math theorem | math_statement =
Let {{math|''A''<sub>1</sub>, ..., ''A''<sub>''n''</sub>}} be independent random points on the plane {{math|'''R'''<sup>2</sup>}} each having the two-dimensional standard normal distribution. Let {{mvar|K<sub>n</sub>}} be the [[convex hull]] of these points, and {{mvar|X<sub>n</sub>}} the area of {{mvar|K<sub>n</sub>}} Then{{sfnp|Bárány|Vu|2007|loc=Theorem 1.1}}

<math display="block"> \frac{ X_n - \operatorname E (X_n) }{ \sqrt{\operatorname{Var} (X_n)} } </math>
converges in distribution to <math display="inline"> \mathcal{N}(0, 1)</math> as {{mvar|n}} tends to infinity.}}

The same also holds in all dimensions greater than 2.

The [[convex polytope|polytope]] {{mvar|K<sub>n</sub>}} is called a Gaussian random polytope.

A similar result holds for the number of vertices (of the Gaussian polytope), the number of edges, and in fact, faces of all dimensions.{{sfnp|Bárány|Vu|2007|loc=Theorem 1.2}}