{
  "id": "1502.01468",
  "version": "v1",
  "published": "2015-02-05T09:15:49.000Z",
  "updated": "2015-02-05T09:15:49.000Z",
  "title": "Brownian Motions with One-Sided Collisions: The Stationary Case",
  "authors": [
    "Patrik L. Ferrari",
    "Herbert Spohn",
    "Thomas Weiss"
  ],
  "comment": "55 pages, 10 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution we consider initial configurations distributed according to a Poisson point process with constant intensity, which makes the process space-time stationary. We prove convergence to the Airy process for stationary the case. As a byproduct we obtain a novel representation of the finite-dimensional distributions of this process. Our method differs from the one used for the TASEP and the KPZ equation by removing the initial step only after the limit $t\\to\\infty$. This leads to a new universal cross-over process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-05T09:15:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motion",
      "stationary case",
      "one-sided collisions",
      "deterministic periodic initial configurations",
      "universal cross-over process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150201468F"
    }
  }
}