{
  "id": "1210.0017",
  "version": "v2",
  "published": "2012-09-28T20:02:41.000Z",
  "updated": "2015-01-16T10:52:42.000Z",
  "title": "A stochastic Burgers equation from a class of microscopic interactions",
  "authors": [
    "Patrícia Gonçalves",
    "Milton Jara",
    "Sunder Sethuraman"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AOP878 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2015, Vol. 43, No. 1, 286-338",
  "doi": "10.1214/13-AOP878",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order $O(n^{-\\gamma})$ for $1/2<\\gamma\\leq1$, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when $\\gamma=1/2$, we show that all limit points satisfy a martingale formulation which may be interpreted in terms of a stochastic Burgers equation derived from taking the gradient of the KPZ equation. The proofs make use of a sharp \"Boltzmann-Gibbs\" estimate which improves on earlier bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-28T20:02:41.000Z",
      "abstract": "We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order $O(n^{-\\gamma})$ for $1/2<\\gamma\\leq 1$, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when $\\gamma = 1/2$, we show that all limit points solve a martingale problem which may be interpreted in terms of a stochastic Burgers equation derived from taking the gradient of the KPZ equation. The proofs make use of a sharp `Boltzmann-Gibbs' estimate which improves on earlier bounds.",
      "comment": "44 pages",
      "journal": null,
      "doi": null,
      "authors": [
        "Patricia Goncalves",
        "Milton Jara",
        "Sunder Sethuraman"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-01-16T10:52:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "35R60"
    ],
    "keywords": [
      "stochastic burgers equation",
      "microscopic interactions",
      "conservative particle systems evolving",
      "weakly asymmetric mass conservative",
      "weak asymmetry"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0017G"
    }
  }
}