Gaussian fluctuations for high-dimensional random projections of ln p-balls

Alonso-Gutiérrez, David (Universidad de Zaragoza) ; Prochno, Joscha ; Thäle, Christoph

Resumen: In 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.

Idioma: Inglés

DOI: 10.3150/18-BEJ1084

Año: 2019

Publicado en: BERNOULLI 25, 4 A (2019), 3139-3174
ISSN: 1350-7265

Factor impacto JCR: 1.496 (2019)

Categ. JCR: STATISTICS & PROBABILITY rank: 45 / 124 = 0.363 (2019) - Q2 - T2

Factor impacto SCIMAGO: 1.993 - Statistics and Probability (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E26-17R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)