Invertibility of symmetric random matrices | Zendy

Vershynin Roman | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Invertibility of symmetric random matrices

Author(s) -

Vershynin Roman

Publication year - 2014

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.20429

Subject(s) - diagonal , mathematics , delocalized electron , spectrum (functional analysis) , combinatorics , random matrix , struct , polynomial , singularity , constant (computer programming) , discrete mathematics , pure mathematics , computer science , physics , quantum mechanics , mathematical analysis , eigenvalues and eigenvectors , geometry , programming language

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 ( − n c ) , 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

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research