{
  "id": "1004.2095",
  "version": "v1",
  "published": "2010-04-13T02:38:26.000Z",
  "updated": "2010-04-13T02:38:26.000Z",
  "title": "Current fluctuations for stochastic particle systems with drift in one spatial dimension",
  "authors": [
    "Timo Seppäläinen"
  ],
  "comment": "70 pages. Material for a minicourse at the 13th Brazilian School of Probability and at the University of Helsinki in August 2009.",
  "journal": "Ensaios Matem{\\'a}ticos, Volume 18 (2010), 1-81",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This review article discusses limit distributions and variance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, independent particles in a random environment, the random average process, the asymmetric simple exclusion process, and a class of totally asymmetric zero range processes. The first three models possess linear macroscopic flux functions and lie in the Edwards-Wilkinson universality class with scaling exponent 1/4 for current fluctuations. For these we prove Gaussian limits for the current process. The latter two systems belong to the Kardar-Parisi-Zhang class. For these we prove the scaling exponent 1/3 in the form of upper and lower variance bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-13T02:38:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F05",
      "60K37"
    ],
    "keywords": [
      "stochastic particle systems",
      "current fluctuations",
      "article discusses limit distributions",
      "asymmetric zero range processes",
      "spatial dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 70,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.2095S"
    }
  }
}