{
  "id": "1608.06256",
  "version": "v1",
  "published": "2016-08-22T18:28:44.000Z",
  "updated": "2016-08-22T18:28:44.000Z",
  "title": "On the $K$-sat model with large number of clauses",
  "authors": [
    "Dmitry Panchenko"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that in the $K$-sat model with $N$ variables and $\\alpha N$ clauses, the expected ratio of the smallest number of unsatisfied clauses to the number of variables is $\\alpha/2^K - \\sqrt{\\alpha} c_*(N)/2^K$ up to smaller order terms $o(\\sqrt{\\alpha})$ as $\\alpha\\to\\infty$ uniformly in $N$, where $c_*(N)$ is the expected normalized maximum energy of some specific mixed $p$-spin spin glass model. The formula for the limit of $c_*(N)$ is well-known from the theory of spin glasses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-22T18:28:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G15",
      "60K35",
      "82B44"
    ],
    "keywords": [
      "sat model",
      "large number",
      "spin spin glass model",
      "smaller order terms",
      "smallest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}