Gaussian averages of interpolated bodies and applications to approximate reconstruction

Authors:
Y. Gordon;A. E. Litvak;S. Mendelson;A. Pajor
Affiliations:
Department of Mathematics, Technion, Haifa 32000, Israel;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1;Department of Mathematics, Technion, Haifa 32000, Israel and Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia;Equipe d'Analyse et Mathématiques Appliquées, Université de Marne-la-Vallée, 5, boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France
Venue:
Journal of Approximation Theory
Year:
2007

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Abstract

We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of B"p^n with @rB"q^n for 1=0, and by the intersection of B"p"~^n with @rB"2^n for 00. We present an application of this result to a statistical problem known as the approximate reconstruction problem.