{
  "id": "1906.04069",
  "version": "v1",
  "published": "2019-06-10T15:20:42.000Z",
  "updated": "2019-06-10T15:20:42.000Z",
  "title": "Stochastic PDE limit of the dynamic ASEP",
  "authors": [
    "Ivan Corwin",
    "Promit Ghosal",
    "Konstantin Matetski"
  ],
  "comment": "60 pages, 1 figure",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face (IRF) model of arXiv:1701.05239, dynamic ASEP has a jump parameter $q\\in (0,1)$ and a dynamical parameter $\\alpha>0$. It degenerates to the standard ASEP height function when $\\alpha$ goes to $0$ or $\\infty$. We consider very weakly asymmetric scaling, i.e., for $\\varepsilon$ tending to zero we set $q=e^{-\\varepsilon}$ and look at fluctuations, space and time in the scales $\\varepsilon^{-1}$, $\\varepsilon^{-2}$ and $\\varepsilon^{-4}$. We show that under such scaling the height function of the dynamic ASEP converges to the solution of the space-time Ornstein-Uhlenbeck process. We also introduce the dynamic ASEP on a ring with generalized rate functions. Under the very weakly asymmetric scaling, we show that the dynamic ASEP (with generalized jump rates) on a ring also converges to the solution of the space-time Ornstein-Uhlenbeck process on $[0,1]$ with periodic boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-10T15:20:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic asep",
      "stochastic pde limit",
      "space-time ornstein-uhlenbeck process",
      "dynamic asymmetric simple exclusion process",
      "standard asep height function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}