Random weighted projections, random quadratic forms and random eigenvectors
Probability
2014-08-19 v2 Combinatorics
Abstract
We present a concentration result concerning random weighted projections in high dimensional spaces. As applications, we prove (1) New concentration inequalities for random quadratic forms; (2) The infinity norm of most unit eigenvectors of a random matrix is of order ; (3) An estimate on the threshold for the local semi-circle law which is tight up to a factor.
Cite
@article{arxiv.1306.3099,
title = {Random weighted projections, random quadratic forms and random eigenvectors},
author = {Van Vu and Ke Wang},
journal= {arXiv preprint arXiv:1306.3099},
year = {2014}
}
Comments
28 pages; re-structured the paper and incorporated the referee's comments and suggestions; to appear, Random Structures & Algorithms