{
  "id": "2109.11532",
  "version": "v1",
  "published": "2021-09-23T17:55:34.000Z",
  "updated": "2021-09-23T17:55:34.000Z",
  "title": "Many nodal domains in random regular graphs",
  "authors": [
    "Shirshendu Ganguly",
    "Theo McKenzie",
    "Sidhanth Mohanty",
    "Nikhil Srivastava"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "cs.DM",
    "math-ph",
    "math.CO",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Let $G$ be a random $d$-regular graph. We prove that for every constant $\\alpha > 0$, with high probability every eigenvector of the adjacency matrix of $G$ with eigenvalue less than $-2\\sqrt{d-2}-\\alpha$ has $\\Omega(n/$polylog$(n))$ nodal domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T17:55:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60B20"
    ],
    "keywords": [
      "random regular graphs",
      "nodal domains",
      "high probability",
      "adjacency matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}