{
  "id": "1707.04927",
  "version": "v1",
  "published": "2017-07-16T18:28:11.000Z",
  "updated": "2017-07-16T18:28:11.000Z",
  "title": "Blocks in the Asymmetric Simple Exclusion Process",
  "authors": [
    "Craig A. Tracy",
    "Harold Widom"
  ],
  "comment": "17 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In earlier work the authors obtained formulas for the probability in the asymmetric simple exclusion process that the $m$th particle from the left is at site $x$ at time $t$. They were expressed in general as sums of multiple integrals and, for the case of step initial condition, as an integral involving a Fredholm determinant. In the present work these results are generalized to the case where the $m$th particle is the left-most one in a contiguous block of $L$ particles. The earlier work depended in a crucial way on two combinatorial identities, and the present work begins with a generalization of these identities to general $L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-16T18:28:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymmetric simple exclusion process",
      "th particle",
      "earlier work",
      "step initial condition",
      "multiple integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}