2017/04/19 by Ilya Soloveychik, Soloveychik, Ilya, Vahid Tarokh +1
Mathematics · #FOS: Mathematics #Graph theory and applications #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #math.PR
paper · pdf · doi:10.48550/arxiv.1704.05890
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
openalex publication_date 2017/04/19 · arxiv created 2017/04/21 · arxiv updated 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.