Random weighted projections, random quadratic forms and random eigenvectors. Issue 4 (2nd July 2014) - Vu, Van; Wang, Ke
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 matrix is of order <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgkrnvkhd4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />O(logn/n)</alternatives>. (3) An estimate on the threshold for the local semi‐circle law which is tight up to a <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgkrnvkh0x" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />logn</alternatives> factor. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 792–821, 2015