A Note on the Concentration of Spectral Measure of Wigner's Matrices
arXiv:1704.05890
Abstract
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.
The authors of the paper arXiv:1101.1923 kindly pointed to us that the results are similar. Unfortunately, we were not aware of their result before. Moreover, our result is sharper in particular regimes, however, we think this is not a significant enough distinction to deserve a separate publication. Therefore, we prefer to withdraw our article