Invertibility of symmetric random matrices1. Issue 2 (11th May 2012) - Vershynin, Roman
Abstract We study n×n symmetric random matrices H, possibly discrete, with iid above‐diagonal entries. We show that H is singular with probability at most exp(−nc), and ||H−1||=O(n). Furthermore, the spectrum of H is delocalized on the optimal scale o(n−1/2). These results improve upon a polynomial singularity bound due to Costello, Tao and Vu, and they generalize, up to constant factors, results of Tao and Vu, and Erdös, Schlein and Yau.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 135‐182, 2014