On generic chaining and the smallest singular value of random matrices with heavy tails Academic Article uri icon

abstract

  • We present a very general chaining method which allows one to control the supremum of the empirical process suphH|N-1i=1Nh2(Xi)-Eh2| in rather general situations. We use this method to establish two main results. First, a quantitative (non-asymptotic) version of the celebrated Bai-Yin Theorem on the singular values of a random matrix with i.i.d. entries that have heavy tails, and second, a sharp estimate on the quadratic empirical process when H={. t, {dot operator}. . :. t. T}, TRn and is an isotropic, unconditional, log-concave measure. 2012 Elsevier Inc.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Mendelson, S., & Paouris, G.

citation count

  • 15

complete list of authors

  • Mendelson, Shahar||Paouris, Grigoris

publication date

  • May 2012