{
  "id": "0905.2993",
  "version": "v2",
  "published": "2009-05-19T12:51:15.000Z",
  "updated": "2010-12-07T13:57:42.000Z",
  "title": "Current fluctuations for TASEP: A proof of the Prähofer--Spohn conjecture",
  "authors": [
    "Gérard Ben Arous",
    "Ivan Corwin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP550 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2011, Vol. 39, No. 1, 104-138",
  "doi": "10.1214/10-AOP550",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities ($\\rho_-,\\rho_+$) are varied, give rise to shock waves and rarefaction fans---the two phenomena which are typical to TASEP. We provide a proof of Conjecture 7.1 of [Progr. Probab. 51 (2002) 185--204] which characterizes the order of and scaling functions for the fluctuations of the height function of two-sided TASEP in terms of the two densities $\\rho_-,\\rho_+$ and the speed $y$ around which the height is observed. In proving this theorem for TASEP, we also prove a fluctuation theorem for a class of corner growth processes with external sources, or equivalently for the last passage time in a directed last passage percolation model with two-sided boundary conditions: $\\rho_-$ and $1-\\rho_+$. We provide a complete characterization of the order of and the scaling functions for the fluctuations of this model's last passage time $L(N,M)$ as a function of three parameters: the two boundary/source rates $\\rho_-$ and $1-\\rho_+$, and the scaling ratio $\\gamma^2=M/N$. The proof of this theorem draws on the results of [Comm. Math. Phys. 265 (2006) 1--44] and extensively on the work of [Ann. Probab. 33 (2005) 1643--1697] on finite rank perturbations of Wishart ensembles in random matrix theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-07T13:57:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "current fluctuations",
      "prähofer-spohn conjecture",
      "passage time",
      "passage percolation model",
      "scaling functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2993B"
    }
  }
}