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000095758 0247_ $$2doi$$a10.1090/proc/15232
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000095758 037__ $$aART-2021-120359
000095758 041__ $$aeng
000095758 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza
000095758 245__ $$aAsymptotic normality for random simplices and convex bodies in high dimensions
000095758 260__ $$c2021
000095758 5060_ $$aAccess copy available to the general public$$fUnrestricted
000095758 5203_ $$aCentral limit theorems for the log-volume of a class of random convex bodies in $ \mathbb{R}^n$ are obtained in the high-dimensional regime, that is, as $ n\to \infty $. In particular, the case of random simplices pinned at the origin and simplices where all vertices are generated at random is investigated. The coordinates of the generating vectors are assumed to be independent and identically distributed with subexponential tails. In addition, asymptotic normality is also established for random convex bodies (including random simplices pinned at the origin) when the spanning vectors are distributed according to a radially symmetric probability measure on the $ n$-dimensional $ \ell _p$-ball. In particular, this includes the cone and the uniform probability measure.
000095758 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000095758 590__ $$a0.971$$b2021
000095758 592__ $$a0.891$$b2021
000095758 594__ $$a1.7$$b2021
000095758 591__ $$aMATHEMATICS$$b166 / 333 = 0.498$$c2021$$dQ2$$eT2
000095758 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1
000095758 591__ $$aMATHEMATICS, APPLIED$$b207 / 267 = 0.775$$c2021$$dQ4$$eT3
000095758 593__ $$aApplied Mathematics$$c2021$$dQ1
000095758 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000095758 700__ $$aBesau, Florian
000095758 700__ $$aGrote, Julian
000095758 700__ $$aKabluchko, Zakhar
000095758 700__ $$aReitzner, Matthias
000095758 700__ $$aThäle, Christoph
000095758 700__ $$aVritsiou Beatrice-Helen
000095758 700__ $$aWerner, Elizabeth
000095758 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000095758 773__ $$g149 (2021), 355-367$$pProc. Am. Math. Soc.$$tPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY$$x0002-9939
000095758 8564_ $$s464082$$uhttps://zaguan.unizar.es/record/95758/files/texto_completo.pdf$$yPostprint
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000095758 951__ $$a2023-05-18-13:29:54
000095758 980__ $$aARTICLE