Invertibility of symmetric random matrices |
| |
| Authors: | Roman Vershynin |
| |
| Affiliation: | Department of Mathematics, University of Michigan, , Ann Arbor, Michigan |
| |
| Abstract: | We study  symmetric random matrices H, possibly discrete, with iid above‐diagonal entries. We show that H is singular with probability at most  , and  . Furthermore, the spectrum of H is delocalized on the optimal scale  . 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 |
| |
| Keywords: | symmetric random matrices invertibility problem singularity probability |
|
|
