{
  "id": "2007.09269",
  "version": "v1",
  "published": "2020-07-17T22:41:23.000Z",
  "updated": "2020-07-17T22:41:23.000Z",
  "title": "The number of saddles of the spherical $p$-spin model",
  "authors": [
    "Antonio Auffinger",
    "Julian Gold"
  ],
  "comment": "52 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the quenched complexity of saddles of the spherical pure $p$-spin model agrees with the annealed complexity when both are positive. Precisely, we show that the second moment of the number of critical values of a given finite index in a given interval has twice the growth rate of the first moment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-17T22:41:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "82D30"
    ],
    "keywords": [
      "spin model",
      "growth rate",
      "finite index",
      "first moment",
      "second moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}