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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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693601
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Submitted on : Wednesday, May 2, 2012 - 6:42:16 PM
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Y. Gordon, A. E. Litvak, S. Mendelson, Alain Pajor. Gaussian averages of interpolated bodies and applications to approximate reconstruction. Journal of Approximation Theory, Elsevier, 2007, 149 (1), pp.59--73. ⟨10.1016/j.jat.2007.04.007⟩. ⟨hal-00693601⟩

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