Dominated concentration

Andreas Maurer

The concentration properties of one random variable may be governed by the values of another random variable which is concentrated and more easily analyzed. We present a general concentration inequality to handle such cases and apply it to the eigenvalues of the Gram matrix for a sample of independent vectors distributed in the unit ball of a Hilbert space. For large samples the deviation of the eigenvalues from their mean is shown to scale with the largest eigenvalue.

Mots clés: Physical Sciences

Andreas Maurer. Dominated concentration. Statistics and Probability Letters, 2010, 80 (7-8), pp.683. ⟨10.1016/j.spl.2009.12.027⟩. ⟨hal-00616895⟩