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Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2014

Tail estimates for norms of sums of log-concave random vectors

Résumé

We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent log-concave random vectors, and uniform versions of these in the form of tail estimates for operator norms of matrices and their sub-matrices in the setting of a log-concave ensemble. This is used to study a quantity A(k, m) that controls uniformly the operator norm of the sub-matrices with k rows and m columns of a matrix A with independent isotropic log-concave random rows. We apply our tail estimates of A(k, m) to the study of restricted isometry property that plays a major role in the compressive sensing theory.

Dates et versions

hal-00794480 , version 1 (26-02-2013)

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Citer

Radosław Adamczak, Rafal Latala, Alexander Litvak, Alain Pajor, Nicole Tomczak-Jaegermann. Tail estimates for norms of sums of log-concave random vectors. Proceedings of the London Mathematical Society, 2014, 108 (Part3), pp.600-637. ⟨10.1112/plms/pdt031⟩. ⟨hal-00794480⟩
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