Random weighted projections, random quadratic forms and random eigenvectors
Copyright policy )Random weighted projections, random quadratic forms and random eigenvectors
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
- University of Minnesota United States
- Hong Kong Polytechnic University China (People's Republic of)
- Yale University United States
- University of Minnesota Morris United States
- Hong Kong University of Science and Technology (香港科技大學) China (People's Republic of)
random covariance matrix, Probability (math.PR), Random matrices (probabilistic aspects), random quadratic forms, Local semi-circle law, Random covariance matrix, local semi-circle law, FOS: Mathematics, Inequalities; stochastic orderings, random weighted projections, Mathematics - Combinatorics, infinity norm of eigenvectors, Combinatorics (math.CO), Infinity norm of eigenvectors, Random linear operators, Mathematics - Probability
random covariance matrix, Probability (math.PR), Random matrices (probabilistic aspects), random quadratic forms, Local semi-circle law, Random covariance matrix, local semi-circle law, FOS: Mathematics, Inequalities; stochastic orderings, random weighted projections, Mathematics - Combinatorics, infinity norm of eigenvectors, Combinatorics (math.CO), Infinity norm of eigenvectors, Random linear operators, Mathematics - Probability
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