On the concentration of measure and the L1-norm

Autores: Yuri Malykhin, K.S. Ryutin
Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 175, Nº 1, 2013, págs. 77-82
Idioma: inglés
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Resumen
- We seek a function in an N-dimensional subspace of L1 that attains a half (more generally, a given part) of its L1-norm on a set of least possible measure. We prove that such a measure is asymptotically maximal when the space is spanned by independent standard normal variables. This answers a question of Y. Benyamini, A. Kro´o, A. Pinkus.