{
  "id": "math/0310044",
  "version": "v2",
  "published": "2003-10-03T18:30:30.000Z",
  "updated": "2005-04-06T07:47:55.000Z",
  "title": "Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks",
  "authors": [
    "Timo Seppalainen"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000000946 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2005, Vol. 33, No. 2, 759-797",
  "doi": "10.1214/009117904000000946",
  "categories": [
    "math.PR"
  ],
  "abstract": "Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n^{1/2} one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuations appear at scale n^{1/4} and converge to a certain self-similar Gaussian process. If the system is in equilibrium, this limiting process specializes to fractional Brownian motion with Hurst parameter 1/4. This contrasts with asymmetric exclusion and Hammersley's process whose second-order fluctuations appear at scale n^{1/3}, as has been discovered through related combinatorial growth models.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-06T07:47:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F17"
    ],
    "keywords": [
      "independent random walks",
      "one-dimensional growth model",
      "second-order fluctuations appear",
      "characteristic",
      "one-dimensional asymmetric system come"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10044S"
    }
  }
}