{
  "id": "1902.01150",
  "version": "v1",
  "published": "2019-02-04T12:33:54.000Z",
  "updated": "2019-02-04T12:33:54.000Z",
  "title": "Estimates of norms of log-concave random matrices with dependent entries",
  "authors": [
    "Marta Strzelecka"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We prove estimates for $\\mathbb{E} \\| X: \\ell_{p'}^n \\to \\ell_q^m\\|$ for $p,q\\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\\le i\\le m, 1\\le j\\le n}$ has i.i.d. isotropic log-concave rows. This generalises the result of Gu\\'edon, Hinrichs, Litvak, and Prochno for Gaussian matrices with independent entries. Our estimate is optimal up to logarithmic factors. As a byproduct we provide the analogue bound for $m\\times n$ random matrices, which entries form an unconditional vector in $\\mathbb{R}^{mn}$. We also prove bounds for norms of matrices which entries are certain Gaussian mixtures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T12:33:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "46B09",
      "15B52"
    ],
    "keywords": [
      "random matrix",
      "log-concave random matrices",
      "isotropic log-concave rows",
      "gaussian matrices",
      "independent entries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}