The volume of random simplices from elliptical distributions in high dimension

Anna Gusakova, Johannes Heiny and Christoph Thäle

Stochastic Processes and their Applications, 2023, vol. 164, issue C, 357-382

Abstract: Random simplices and more general random convex bodies of dimension p in Rn 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.

Keywords: Central limit theorem; Elliptical distribution; Logarithmic volume; Random determinant; Random simplex; Stochastic geometry in high dimensions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.07.012

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