Geometry of log-concave Ensembles of random matrices and approximate reconstruction

Radosław Adamczak; Rafał Latała; Alexander E. Litvak; Alain Pajor; Nicole Tomczak-Jaegermann

doi:10.1016/j.crma.2011.06.025

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arXiv · 1103.0401

Geometry of log-concave Ensembles of random matrices and approximate reconstruction

Radosław Adamczak·Rafał Latała·Alexander E. Litvak·Alain Pajor·Nicole Tomczak-Jaegermann

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Abstract

We study the Restricted Isometry Property of a random matrix $Γ$ with independent isotropic log-concave rows. To this end, we introduce a parameter $Γ_{k,m}$ that controls uniformly the operator norm of sub-matrices with $k$ rows and $m$ columns. This parameter is estimated by means of new tail estimates of order statistics and deviation inequalities for norms of projections of an isotropic log-concave vector.

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Radosław Adamczak, Rafał Latała, Alexander E. Litvak, Alain Pajor, Nicole Tomczak-Jaegermann. 2011-03-02. Geometry of log-concave Ensembles of random matrices and approximate reconstruction. https://doi.org/10.1016/j.crma.2011.06.025

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