{
  "id": "1306.5095",
  "version": "v2",
  "published": "2013-06-21T11:09:04.000Z",
  "updated": "2015-04-22T13:39:00.000Z",
  "title": "Scaling limit for Brownian motions with one-sided collisions",
  "authors": [
    "Patrik L. Ferrari",
    "Herbert Spohn",
    "Thomas Weiss"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/14-AAP1025 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2015, Vol. 25, No. 3, 1349-1382",
  "doi": "10.1214/14-AAP1025",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\\\"{u}tz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy$_1$ process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-21T11:09:04.000Z",
      "title": "Scaling Limit for Brownian Motions with One-sided Collisions",
      "abstract": "We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\\\"utz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, i.e., particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy_1 process.",
      "comment": "28 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-22T13:39:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motions",
      "one-sided collisions",
      "appropriate large time scaling limit",
      "periodic initial configuration",
      "signed determinantal point process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5095F"
    }
  }
}