English

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 ±1\pm 1 matrix is of order O(logn/n)O( \sqrt { \log n/n}); (3) An estimate on the threshold for the local semi-circle law which is tight up to a logn\sqrt {\log n} factor.

Keywords

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

R2 v1 2026-06-22T00:33:17.789Z