{
  "id": "1309.6068",
  "version": "v2",
  "published": "2013-09-24T07:48:06.000Z",
  "updated": "2016-02-11T06:35:52.000Z",
  "title": "Off-Criticality and the Massive Brownian Loop Soup",
  "authors": [
    "Federico Camia"
  ],
  "comment": "V2: 23 pages, added result, revised presentation",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a natural \"massive\" version of the Brownian loop soup of Lawler and Werner which displays conformal covariance and exponential decay. We show that this massive Brownian loop soup arises as the near-critical scaling limit of a random walk loop soup with killing and is related to the massive SLE(2) identified by Makarov and Smirnov as the near-critical scaling limit of a loop-erased random walk with killing. We conjecture that the massive Brownian loop soup describes the zero level lines of the massive Gaussian free field, and discuss possible relations to other models, such as Ising, in the off-critical regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-24T07:48:06.000Z",
      "abstract": "The Brownian loop soup is a conformally invariant Poissonian ensemble of loops in the plane recently introduced by Lawler and Werner. It has attracted significant attention for its connection to the Schramm-Loewner Evolution and Conformal Loop Ensembles and its consequent ability to describe the critical scaling limit of two-dimensional statistical mechanical models. In this paper, we introduce a natural \"massive\" (non-scale-invariant) version of the Brownian loop soup as a candidate to describe near-critical scaling limits, and study some of its properties, such as conformal covariance, exponential decay of correlations, and Hausdorff dimension. We also show that the massive Brownian loop soup arises as the near-critical scaling limit of a \"gas\" of random walk loops which is closely related to the discrete Gaussian free field.",
      "comment": "38 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-11T06:35:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "82B41",
      "60K35",
      "81T40"
    ],
    "keywords": [
      "discrete gaussian free field",
      "off-criticality",
      "near-critical scaling limit",
      "massive brownian loop soup arises",
      "random walk loops"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6068C"
    }
  }
}