{
  "id": "1607.08684",
  "version": "v1",
  "published": "2016-07-29T04:06:38.000Z",
  "updated": "2016-07-29T04:06:38.000Z",
  "title": "Phase Transitions in the ASEP and Stochastic Six-Vertex Model",
  "authors": [
    "Amol Aggarwal",
    "Alexei Borodin"
  ],
  "comment": "64 pages, 11 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we consider two models in the Kardar-Parisi-Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call {\\itshape generalized step Bernoulli initial data}) for both of these models that generalizes the step Bernoulli initial data studied in a number of recent works on the ASEP. Under this class of initial data, we analyze the current fluctuations of both the ASEP and stochastic six-vertex model and establish the existence of a phase transition along a characteristic line, across which the fluctuation exponent changes from $1 / 2$ to $1 / 3$. On the characteristic line, the current fluctuations converge to the general (rank $k$) Baik-Ben-Arous-P\\'{e}ch\\'{e} distribution for the law of the largest eigenvalue of a critically spiked covariance matrix. For $k = 1$, this was established for the ASEP by Tracy and Widom; for $k > 1$ (and also $k = 1$, for the stochastic six-vertex model), the appearance of these distributions in both models is new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T04:06:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic six-vertex model",
      "phase transition",
      "asymmetric simple exclusion process",
      "generalized step bernoulli initial data",
      "characteristic line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}