The volume of random simplices from elliptical distributions in high dimension

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.

Heiny, Johannes,1989-Stockholms universitet,Matematiska institutionen(Swepub:su)johe3032 (författare)
Thäle, Christoph (författare)
Stockholms universitetMatematiska institutionen (creator_code:org_t)

Ingår i:Stochastic Processes and their Applications164, s. 357-3820304-41491879-209X

Av författaren/redakt...: Gusakova, Anna; Heiny, Johannes, ...; Thäle, Christoph

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