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 matrix is of order O(log n/n). (3) An estimate on the threshold for the local semi-circle law which is tight up to a logn factor.
- Infinity norm of eigenvectors
- Local semi-circle law
- Random covariance matrix
- Random quadratic forms
- Random weighted projections