On the spectral norm of Gaussian random matrices

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Let X be a d × d symmetric random matrix with independent but nonidentically distributed Gaussian entries. It has been conjectured by Lata̷la that the spectral norm of X is always of the same order as the largest Euclidean norm of its rows. A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous Gaussian random matrices. This paper establishes the conjecture up to a dimensional factor of order √log log d. Moreover, dimension-free bounds are developed that are optimal to leading order and that establish the conjecture in special cases. The proofs of these results shed significant light on the geometry of the underlying Gaussian processes.

Original languageEnglish (US)
Pages (from-to)8161-8178
Number of pages18
JournalTransactions of the American Mathematical Society
Volume369
Issue number11
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Nonasymptotic bounds
  • Random matrices
  • Spectral norm

Fingerprint Dive into the research topics of 'On the spectral norm of Gaussian random matrices'. Together they form a unique fingerprint.

  • Cite this