{
  "id": "1104.3752",
  "version": "v1",
  "published": "2011-04-19T14:04:35.000Z",
  "updated": "2011-04-19T14:04:35.000Z",
  "title": "Recursive structures in the multispecies TASEP",
  "authors": [
    "Chikashi Arita",
    "Arvind Ayyer",
    "Kirone Mallick",
    "Sylvain Prolhac"
  ],
  "journal": "J. Phys. A: Math. Theor. 44 (2011) 335004",
  "doi": "10.1088/1751-8113/44/33/335004",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a multi-species generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for x and yth-class particles (x<y), the transition xy -> yx occurs with a rate independent from the values x and y. P. A. Ferrari and J. Martin (2007) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al. (2009). This `matrix ansatz' shows that the stationary state of the multi-species TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N-1)-TASEP stationary state. Besides, Arita et al. (2009) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N-1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N-1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari-Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-19T14:04:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary state",
      "multispecies tasep",
      "recursive structures",
      "matrix product representation",
      "fact intertwines markov matrices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Aug",
      "volume": 44,
      "number": 33,
      "pages": 335004
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44G5004A"
    }
  }
}