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- Gusakova, Anna, et al.
(author)
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The volume of random simplices from elliptical distributions in high dimension
- 2023
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In: Stochastic Processes and their Applications. - 0304-4149 .- 1879-209X. ; 164, s. 357-382
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Journal article (peer-reviewed)abstract
- Random simplices and more general random convex bodies of dimension p in 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 whose rows are copies of a random vector with an elliptical distribution, which is established as well.
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