# The volume of random simplices from elliptical distributions in high dimension

@inproceedings{Gusakova2022TheVO, title={The volume of random simplices from elliptical distributions in high dimension}, author={Anna Gusakova and Johannes Heiny and Christoph Thale}, year={2022} }

Random simplices and more general random convex bodies of dimension p in R with p ≤ n are considered, which are generated by random vectors having an elliptical distribution. In the high-dimensional regime, that is, if p → ∞ and n → ∞ in such a way that p/n → γ ∈ (0, 1), a central and a stable limit theorem for the logarithmic volume of random simplices and random convex bodies is shown. The result follows from a related central limit theorem for the log-determinant of p × n random matrices…

## One Citation

### Limit theorems for the volumes of small codimensional random sections of $\ell_p^n$-balls

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. We establish Central Limit Theorems for the volumes of intersections of B np (the unit ball of ℓ np ) with uniform random subspaces of codimension d for ﬁxed d and n → ∞ . As a corollary we obtain…

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