{
  "id": "1906.10674",
  "version": "v1",
  "published": "2019-06-25T17:24:47.000Z",
  "updated": "2019-06-25T17:24:47.000Z",
  "title": "Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices",
  "authors": [
    "Serban Belinschi",
    "Charles Bordenave",
    "Mireille Capitaine",
    "Guillaume Cébron"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a square random matrix of size $N$ of the form $P(Y,A)$ where $P$ is a noncommutative polynomial, $A$ is a tuple of deterministic matrices converging in $\\ast$-distribution, when $N$ goes to infinity, towards a tuple $a$ in some $\\mathcal{C}^*$-probability space and $Y$ is a tuple of independent matrices with i.i.d. centered entries with variance $1/N$. We investigate the eigenvalues of $P(Y,A)$ outside the spectrum of $P(c,a)$ where $c$ is a circular system which is free from $a$. We provide a sufficient condition to guarantee that these eigenvalues coincide asymptotically with those of $P(0,A)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-25T17:24:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deterministic matrices",
      "outlier eigenvalues",
      "non-hermitian polynomials",
      "square random matrix",
      "eigenvalues coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}