Random weighted projections, random quadratic forms and random eigenvectors

Van Vu, Ke Wang

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)792-821
Number of pages30
JournalRandom Structures and Algorithms
Issue number4
StatePublished - Dec 2015


  • Infinity norm of eigenvectors
  • Local semi-circle law
  • Random covariance matrix
  • Random quadratic forms
  • Random weighted projections


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