{
  "id": "1405.5146",
  "version": "v2",
  "published": "2014-05-20T16:23:38.000Z",
  "updated": "2015-01-28T13:33:58.000Z",
  "title": "Existence of Ground States of Nonlocal-Interaction Energies",
  "authors": [
    "Robert Simione",
    "Dejan Slepčev",
    "Ihsan Topaloglu"
  ],
  "comment": "This version is to appear in the J Stat Phys",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. $H$-stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-20T16:23:38.000Z",
      "title": "Existence of Minimizers of Nonlocal Interaction Energies",
      "abstract": "We investigate nonlocal-interaction energies on the space of probability measures. We establish sharp conditions for the existence of minimizers for a broad class of nonlocal-interaction energies. The condition is closely related to the notion of $H$-stability of pairwise interaction potentials in statistical mechanics. Our approach uses the direct method of calculus of variations.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-28T13:33:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "82B21",
      "82B05",
      "35R09",
      "45K05"
    ],
    "keywords": [
      "nonlocal interaction energies",
      "minimizers",
      "nonlocal-interaction energies",
      "establish sharp conditions",
      "direct method"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-015-1215-z",
      "journal": "Journal of Statistical Physics",
      "year": 2015,
      "month": "May",
      "pages": 972,
      "volume": 159,
      "number": 4
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JSP...159..972S"
    }
  }
}