Isotropic self-consistent equations for mean-field random matrices

Yukun He, Antti Knowles, Ron Rosenthal

Research output: Contribution to journalArticlepeer-review


We present a simple and versatile method for deriving (an)isotropic local laws for general random matrices constructed from independent random variables. Our method is applicable to mean-field random matrices, where all independent variables have comparable variances. It is entirely insensitive to the expectation of the matrix. In this paper we focus on the probabilistic part of the proof—the derivation of the self-consistent equations. As a concrete application, we settle in complete generality the local law for Wigner matrices with arbitrary expectation.

Original languageEnglish
Pages (from-to)203-249
Number of pages47
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - 1 Jun 2018


  • 15B52
  • 82B44
  • 82C44

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Isotropic self-consistent equations for mean-field random matrices'. Together they form a unique fingerprint.

Cite this