On the Gaussian behavior of marginals and the mean width of random polytopes
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 / 311 = 0.395 (2015) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 156 / 254 = 0.614 (2015) - Q3 - T2

Factor impacto SCIMAGO:

Tipo y forma: Article (PrePrint)
Área (Departamento): Análisis Matemático (Departamento de Matemáticas)

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