{
  "id": "1412.3911",
  "version": "v1",
  "published": "2014-12-12T07:58:43.000Z",
  "updated": "2014-12-12T07:58:43.000Z",
  "title": "Edwards-Wilkinson fluctuations in the Howitt-Warren flows",
  "authors": [
    "Jinjiong Yu"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study current fluctuations in a one-dimensional interacting particle system known as the dual smoothing process that is dual to random motions in a Howitt-Warren flow. The Howitt-Warren flow can be regarded as the transition kernels of a random motion in a continuous space-time random environment. It turns out that the current fluctuations of the dual smoothing process fall in the Edwards-Wilkinson universality class, where the fluctuations occur on the scale $t^{1/4}$ and the limit is a universal Gaussian process. Along the way, we prove a quenched invariance principle for a random motion in the Howitt-Warren flow. Meanwhile, the centered quenched mean process of the random motion also converges on the scale $t^{1/4}$, where the limit is another universal Gaussian process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-12T07:58:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "60F17"
    ],
    "keywords": [
      "howitt-warren flow",
      "edwards-wilkinson fluctuations",
      "random motion",
      "universal gaussian process",
      "edwards-wilkinson universality class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3911Y"
    }
  }
}