Moment inequalities and central limit properties of isotropic convex bodies |
| |
Authors: | Ulrich Brehm Peter Hinow Hendrik Vogt Jürgen Voigt |
| |
Affiliation: | Fachrichtung Mathematik, Technische Universit?t Dresden, 01062 Dresden, Germany (e-mail: {brehm;vogt;voigt}@math.tu-dresden.de), DE
|
| |
Abstract: | The object of our investigations are isotropic convex bodies , centred at the origin and normed to volume one, in arbitrary dimensions. We show that a certain subset of these bodies – specified by bounds on the second and fourth moments – is invariant under forming ‘expanded joinsrsquo;. Considering a body K as above as a probability space and taking , we define random variables on K. It is known that for subclasses of isotropic convex bodies satisfying a ‘concentration of mass property’, the distributions of these random variables are close to Gaussian distributions, for high dimensions n and ‘most’ directions . We show that this ‘central limit property’, which is known to hold with respect to convergence in law, is also true with respect to -convergence and -convergence of the corresponding densities. Received: 21 March 2001 / in final form: 17 October 2001 / Published online: 4 April 2002 |
| |
Keywords: | Mathematics Subject Classification (2000): 52A20 60F25 26B25 |
本文献已被 SpringerLink 等数据库收录! |
|