{
  "id": "0808.3037",
  "version": "v1",
  "published": "2008-08-22T07:48:54.000Z",
  "updated": "2008-08-22T07:48:54.000Z",
  "title": "Limit laws for the energy of a charged polymer",
  "authors": [
    "Xia Chen"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AIHP120 the Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annales de l'Institut Henri Poincar\\'e - Probabilit\\'es et Statistiques 2008, Vol. 44, No. 4, 638-672",
  "doi": "10.1214/07-AIHP120",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy \\[H_n=\\sum_{1\\le j<k\\le n}\\omega_j\\omega_k1_{\\{S_j=S_k\\}}\\] of the polymer $\\{S_1,...,S_n\\}$ equipped with random electrical charges $\\{\\omega_1,...,\\omega_n\\}$. Our approach is based on comparison of the moments between $H_n$ and the self-intersection local time \\[Q_n=\\sum_{1\\le j<k\\le n}1_{\\{S_j=S_k\\}}\\] run by the $d$-dimensional random walk $\\{S_k\\}$. As partially needed for our main objective and partially motivated by their independent interest, the central limit theorems and exponential integrability for $Q_n$ are also investigated in the case $d\\ge3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-22T07:48:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit laws",
      "charged polymer",
      "central limit theorems",
      "self-intersection local time",
      "dimensional random walk"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008AnIHP..44..638C"
    }
  }
}