Variance estimates and almost Euclidean structure Academic Article uri icon


  • Abstract We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on n , which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the importance of the statistical measures of dispersion of the norm in connection with the local structure of the ambient space. As a byproduct of our study, we provide a short proof of Dvoretzkys theorem which not only supports the aforementioned significance but also complements the classical probabilistic formulation.

published proceedings


author list (cited authors)

  • Paouris, G., & Valettas, P.

citation count

  • 4

complete list of authors

  • Paouris, Grigoris||Valettas, Petros

publication date

  • January 2019