Gaussian averages of interpolated bodies and applications to approximate reconstruction

Abstract : 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.