{
  "id": "1907.09155",
  "version": "v1",
  "published": "2019-07-22T06:56:13.000Z",
  "updated": "2019-07-22T06:56:13.000Z",
  "title": "Mapping TASEP back in time",
  "authors": [
    "Leonid Petrov",
    "Axel Saenz"
  ],
  "comment": "42 pages, 12 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We obtain a new relation between the distributions $\\mu_t$ at different times $t\\ge 0$ of the continuous-time TASEP (Totally Asymmetric Simple Exclusion Process) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $\\mu_t$ backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $\\mu_t$ which in turn brings new identities for expectations with respect to $\\mu_t$. The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang-Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T06:56:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping tasep",
      "totally asymmetric simple exclusion process",
      "step initial configuration",
      "continuous-time markov process",
      "markov maps interchanging parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}