English

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

Probability 2015-01-06 v1 Functional Analysis Metric Geometry

Abstract

We study the Restricted Isometry Property of a random matrix Γ\Gamma with independent isotropic log-concave rows. To this end, we introduce a parameter Γk,m\Gamma_{k,m} that controls uniformly the operator norm of sub-matrices with kk rows and mm 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.

Keywords

Cite

@article{arxiv.1103.0401,
  title  = {Geometry of log-concave Ensembles of random matrices and approximate reconstruction},
  author = {Radosław Adamczak and Rafał Latała and Alexander E. Litvak and Alain Pajor and Nicole Tomczak-Jaegermann},
  journal= {arXiv preprint arXiv:1103.0401},
  year   = {2015}
}