{
  "id": "1903.08135",
  "version": "v1",
  "published": "2019-03-19T17:46:52.000Z",
  "updated": "2019-03-19T17:46:52.000Z",
  "title": "A Local Limit Theorem and Delocalization of Eigenvectors for Polynomials in Two Matrices",
  "authors": [
    "Ching-Wei Ho"
  ],
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We propose a boundary regularity condition for the $M_n(\\C)$-valued subordination functions in free probability to prove the local limit theorem and delocalization of eigenvectors for polynomials in two random matrices. We prove this through estimating the pair of $M_n(\\C)$-valued approximate subordination functions for the sum of two $M_n(\\C)$-valued random matrices $\\gamma_1\\tensor C_N+\\gamma_2\\tensor U_N^*D_NU_N$, where $C_N$, $D_N$ are deterministic diagonal matrices, and $U_N$ is Haar unitary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-19T17:46:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local limit theorem",
      "delocalization",
      "eigenvectors",
      "polynomials",
      "deterministic diagonal matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}