Invertibility of symmetric random matrices


  • Partially supported by NSF Grant (DMS 1001829)


We study math formula symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most math formula, and math formula. Furthermore, the spectrum of H is delocalized on the optimal scale math formula. 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