Singularities of the density of states of random Gram matrices Journal Article


Author(s): Alt, Johannes
Article Title: Singularities of the density of states of random Gram matrices
Affiliation IST Austria
Abstract: For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities.
Keywords: Local law; general variance profile; Cubic cusp; Dyson equation; square-root edge
Journal Title: Electronic Communications in Probability
Volume: 22
ISSN: 1083-589X
Publisher: Institute of Mathematical Statistics  
Date Published: 2017-11-21
Start Page: Article number: 63
Copyright Statement: CC BY 4.0
Sponsor: ERC Advanced Grant RANMAT No. 338804
URL:
DOI: 10.1214/17-ECP97
Open access: yes (OA journal)