{
  "id": "1508.01101",
  "version": "v1",
  "published": "2015-08-05T15:17:04.000Z",
  "updated": "2015-08-05T15:17:04.000Z",
  "title": "Weak convergence of the empirical spectral distribution of high-dimensional banded sample covariance matrices",
  "authors": [
    "Kamil Jurczak"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\\to 0 \\ \\ \\text{and} \\ \\ 2d/n\\to y>0.$$ It is shown that the empirical spectral distribution of those matrices almost surely converges weakly to some deterministic probability measure which is characterized by its moments. Certain restricted compositions of natural numbers play a crucial role in the evaluation of the expected moments of the empirical spectral distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-05T15:17:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-dimensional banded sample covariance matrices",
      "empirical spectral distribution",
      "weak convergence",
      "deterministic probability measure",
      "natural numbers play"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}