  In this short note we derive concentration inequalities for the empirical
absolute moments of square symmetric matrices with independent symmetrically
distributed +/-1 entries. Most of the previous results of this type are limited
to functions with bounded Lipschitz constant, and therefore exclude the moments
from consideration. Based on the fine analysis of the distribution of the
largest eigenvalues developed by Soshnikov and Sinai, we extend the measure
concentration tools of Talagrand to encompass power functions.
