{
  "id": "2208.11952",
  "version": "v1",
  "published": "2022-08-25T09:15:55.000Z",
  "updated": "2022-08-25T09:15:55.000Z",
  "title": "At the edge of a cloud of Brownian particles",
  "authors": [
    "Dom Brockington",
    "Jon Warren"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a simple model for the trajectory of a particle in a turbulent fluid, where a Brownian motion travels through a random Gaussian velocity field. We study the quenched law of the process and prove that in a weak environment setting, the fluctuations at the transition from weak to strong disorder are described by the KPZ equation. We conjecture the same is true without the assumption of a weak environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-25T09:15:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian particles",
      "weak environment",
      "random gaussian velocity field",
      "brownian motion travels",
      "turbulent fluid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}