{
  "id": "2104.02662",
  "version": "v1",
  "published": "2021-04-06T16:49:54.000Z",
  "updated": "2021-04-06T16:49:54.000Z",
  "title": "The spectral norm of Gaussian matrices with correlated entries",
  "authors": [
    "Afonso S. Bandeira",
    "March T. Boedihardjo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a non-asymptotic bound on the spectral norm of a $d\\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\\sqrt{\\log d}$ factor in the noncommutative Khintchine inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-06T16:49:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral norm",
      "gaussian matrices",
      "correlated entries",
      "non-asymptotic bound",
      "noncommutative khintchine inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}