Gaussian averages of interpolated bodies and applications to approximate reconstruction

Y. Gordon (1) , A. E. Litvak , S. Mendelson (1) , Alain Pajor (2)

1 TECHNION - Department of Mathematics
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of B-p(n) with rho B-q(n) for 1 <= p, q <= infinity and rho > 0, and by the intersection of B-p infinity(n) with rho B-2(n) for 0 < p <= 1 and rho > 0. We present an application of this result to a statistical problem known as the approximate reconstruction problem. (c) 2007 Elsevier Inc. All rights reserved.

Domaines: Physique mathématique [math-ph]

Y. Gordon, A. E. Litvak, S. Mendelson, Alain Pajor. Gaussian averages of interpolated bodies and applications to approximate reconstruction. Journal of Approximation Theory, 2007, 149 (1), pp.59--73. ⟨10.1016/j.jat.2007.04.007⟩. ⟨hal-00693601⟩