Random weighted projections, random quadratic forms and random eigenvectors

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

28 pages; re-structured the paper and incorporated the referee's comments and suggestions; to appear, Random Structures & Algorithms

References in corpus (2)

• Local semicircle law and complete delocalization for Wigner random matrices
• Hanson-Wright inequality and sub-gaussian concentration

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