{
  "id": "1504.00614",
  "version": "v1",
  "published": "2015-04-02T16:53:26.000Z",
  "updated": "2015-04-02T16:53:26.000Z",
  "title": "Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions",
  "authors": [
    "Sergio Caracciolo",
    "Gabriele Sicuro"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We analyze the random Euclidean bipartite matching problem on the hypertorus in $d$ dimensions with quadratic cost and we derive the two--point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo et al. to evaluate the average optimal matching cost. We consider both the grid--Poisson matching problem and the Poisson--Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-02T16:53:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scaling hypothesis",
      "random euclidean bipartite matching problem",
      "two-point correlation function",
      "average optimal matching cost",
      "hypertorus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}