000084733 001__ 84733
000084733 005__ 20200716101539.0
000084733 0247_ $$2doi$$a10.3150/18-BEJ1084
000084733 0248_ $$2sideral$$a114059
000084733 037__ $$aART-2019-114059
000084733 041__ $$aeng
000084733 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso-Gutiérrez, David$$uUniversidad de Zaragoza
000084733 245__ $$aGaussian fluctuations for high-dimensional random projections of ln p-balls
000084733 260__ $$c2019
000084733 5060_ $$aAccess copy available to the general public$$fUnrestricted
000084733 5203_ $$aIn this paper, we study high-dimensional random projections of ln p-balls. More precisely, for any n ¿ N let En be a random subspace of dimension kn ¿ {1, . . ., n} and Xn be a random point in the unit ball of ln p. Our work provides a description of the Gaussian fluctuations of the Euclidean norm ||PEnXn|| 2 of random orthogonal projections of Xn onto En. In particular, under the condition that kn ¿ 8 it is shown that these random variables satisfy a central limit theorem, as the space dimension n tends to infinity. Moreover, if kn ¿ 8 fast enough, we provide a Berry-Esseen bound on the rate of convergence in the central limit theorem. At the end, we provide a discussion of the large deviations counterpart to our central limit theorem.
000084733 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E26-17R$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P
000084733 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000084733 590__ $$a1.496$$b2019
000084733 591__ $$aSTATISTICS & PROBABILITY$$b45 / 124 = 0.363$$c2019$$dQ2$$eT2
000084733 592__ $$a1.993$$b2019
000084733 593__ $$aStatistics and Probability$$c2019$$dQ1
000084733 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000084733 700__ $$aProchno, Joscha
000084733 700__ $$aThäle, Christoph
000084733 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000084733 773__ $$g25, 4 A (2019), 3139-3174$$pBernoulli$$tBERNOULLI$$x1350-7265
000084733 8564_ $$s485826$$uhttps://zaguan.unizar.es/record/84733/files/texto_completo.pdf$$yVersión publicada
000084733 8564_ $$s100383$$uhttps://zaguan.unizar.es/record/84733/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000084733 909CO $$ooai:zaguan.unizar.es:84733$$particulos$$pdriver
000084733 951__ $$a2020-07-16-09:38:39
000084733 980__ $$aARTICLE