ASYMPTOTIC NORMALITY FOR RANDOM SIMPLICES AND CONVEX BODIES IN HIGH DIMENSIONS
DC Element | Wert | Sprache |
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dc.contributor.author | Alonso-Gutierrez, D. | |
dc.contributor.author | Besau, F. | |
dc.contributor.author | Grote, J. | |
dc.contributor.author | Kabluchko, Z. | |
dc.contributor.author | Reitzner, M. | |
dc.contributor.author | Thale, C. | |
dc.contributor.author | Vritsiou, B-H | |
dc.contributor.author | Werner, E. | |
dc.date.accessioned | 2021-12-23T16:23:28Z | - |
dc.date.available | 2021-12-23T16:23:28Z | - |
dc.date.issued | 2021 | |
dc.identifier.issn | 00029939 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/14550 | - |
dc.description.abstract | Central limit theorems for the log-volume of a class of random convex bodies in R-n are obtained in the high-dimensional regime, that is, as n -> infinity. 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 (s)ymmetric probability measure on the n-dimensional l(p)-ball. In particular, this includes the cone and the uniform probability measure. | |
dc.description.sponsorship | MICIN Project [PID2019-105979GB-I00]; DGA Project [E48_20R]; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [BE 2484/5-2]; DFGGerman Research Foundation (DFG)European Commission [RTG 2131]; DFG under Germany's Excellence StrategyGerman Research Foundation (DFG) [EXC 2044 390685587]; NSFNational Science Foundation (NSF) [DMS-1811146]; The first author was partially supported by MICIN Project PID2019-105979GB-I00 and DGA Project E48_20R.; The second author was partially supported by the Deutsche Forschungsgemeinschaft (DFG) grant BE 2484/5-2.; The third author was supported by DFG via RTG 2131 ``High-dimensional Phenomena in Probability - Fluctuations and Discontinuity''.; The fourth athor was supported by DFG under Germany's Excellence Strategy EXC 2044 390685587.; The eighth author was partially supported by NSF grant DMS-1811146. | |
dc.language.iso | en | |
dc.publisher | AMER MATHEMATICAL SOC | |
dc.relation.ispartof | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | |
dc.subject | BALL | |
dc.subject | Central limit theorem | |
dc.subject | high dimensions | |
dc.subject | l(p)-ball | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | random convex body | |
dc.subject | random determinant | |
dc.subject | random parallelotope | |
dc.subject | random polytope | |
dc.subject | random simplex | |
dc.subject | stochastic geometry | |
dc.subject | VOLUME | |
dc.title | ASYMPTOTIC NORMALITY FOR RANDOM SIMPLICES AND CONVEX BODIES IN HIGH DIMENSIONS | |
dc.type | journal article | |
dc.identifier.doi | 10.1090/proc/15232 | |
dc.identifier.isi | ISI:000600416300031 | |
dc.description.volume | 149 | |
dc.description.issue | 1 | |
dc.description.startpage | 355 | |
dc.description.endpage | 367 | |
dc.contributor.orcid | 0000-0003-1256-3671 | |
dc.contributor.researcherid | AAT-6303-2021 | |
dc.identifier.eissn | 10886826 | |
dc.publisher.place | 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA | |
dcterms.isPartOf.abbreviation | Proc. Amer. Math. Soc. | |
dcterms.oaStatus | Green Accepted, hybrid, Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | ReMa759 | - |
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geprüft am 23.05.2024