{
  "id": "1605.00691",
  "version": "v1",
  "published": "2016-05-02T21:32:15.000Z",
  "updated": "2016-05-02T21:32:15.000Z",
  "title": "A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality",
  "authors": [
    "Jeffrey Kuan"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "This paper introduces a multi-species version of a process called ASEP(q,j). In this process, up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry 0<q^{2j}<1, and there are n-1 species of particles in which heavier particles can force lighter particles to switch places. Assuming closed boundary conditions, we explicitly write the reversible measures and a self-duality function, generalizing previously known results for two-species ASEP and single-species ASEP(q,j). Additionally, it is shown that this multi-species ASEP(q,j) is dual to its space-reversed version, in which particles drift to the left. As j goes to infinity, this multi-species ASEP(q,j) converges to a multi-species q-TAZRP and the self-duality function has a non-trivial limit, showing that this multi-species q-TAZRP satisfies a space-reversed self-duality. The construction of the process and the proofs are accomplished utilizing spin j representations of U_q(gl_n), extending the approach used for single-species ASEP(q,j).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-02T21:32:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-species asep",
      "stochastic duality",
      "particles drift",
      "self-duality function",
      "single-species asep"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}