On the Gaussian behavior of marginals and the mean width of random polytopes

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

Resumen: We show that the expected value of the mean width of a random polytope generated by $ N$ random vectors ( $ n\leq N\leq e^{\sqrt n}$) uniformly distributed in an isotropic convex body in $ \mathbb{R}^n$ is of the order $ \sqrt {\log N} L_K$. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way.

Idioma: Inglés

DOI: 10.1090/S0002-9939-2014-12401-4

Año: 2015

Publicado en: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 143 (2015), 821-832
ISSN: 0002-9939

Factor impacto JCR: 0.7 (2015)

Categ. JCR: MATHEMATICS rank: 123 / 312 = 0.394 (2015) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 156 / 254 = 0.614 (2015) - Q3 - T2

Factor impacto SCIMAGO: 1.099 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q2)

Tipo y forma: Article (PrePrint)

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