{
  "id": "2401.02815",
  "version": "v1",
  "published": "2024-01-05T13:55:15.000Z",
  "updated": "2024-01-05T13:55:15.000Z",
  "title": "On the empirical spectral distribution of large wavelet random matrices based on mixed-Gaussian fractional measurements in moderately high dimensions",
  "authors": [
    "Patrice Abry",
    "Gustavo Didier",
    "Oliver Orejola",
    "Herwig Wendt"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and, for a fixed integer $j$, the scale $a(n)2^j$ go to infinity in such a way that $\\lim_{n \\rightarrow \\infty}p(n)\\cdot a(n)/n = \\lim_{n \\rightarrow \\infty} o(\\sqrt{a(n)/n})= 0$. We suppose the underlying measurement process is a random scrambling of a sample of size $n$ of a growing number $p(n)$ of fractional processes. Each of the latter processes is a fractional Brownian motion conditionally on a randomly chosen Hurst exponent. We show that the (rescaled logarithmic) empirical spectral distribution of the wavelet random matrices converges weakly, in probability, to the distribution of Hurst exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-05T13:55:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "empirical spectral distribution",
      "large wavelet random matrices",
      "mixed-gaussian fractional measurements",
      "moderately high dimensions",
      "random matrices converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}