{
  "id": "1810.10650",
  "version": "v1",
  "published": "2018-10-24T23:03:41.000Z",
  "updated": "2018-10-24T23:03:41.000Z",
  "title": "Stationary distributions of the multi-type ASEP",
  "authors": [
    "James B. Martin"
  ],
  "comment": "52 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of \"multi-line diagrams\" or systems of queues in tandem. Let $q$ be the asymmetry parameter of the system. The queueing construction generalises the one previously known for the totally asymmetric ($q=0$) case, by introducing queues in which each potential service is unused with probability $q^k$ when the queue-length is $k$. The analysis is based on the matrix product representation of Prolhac, Evans and Mallick. Consequences of the construction include: a simple method for sampling exactly from the stationary distribution for the system on a ring; results on common denominators of the stationary probabilities, expressed as rational functions of $q$ with non-negative integer coefficients; and probabilistic descriptions of \"convoy formation\" phenomena in large systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-24T23:03:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary distribution",
      "multi-type asep",
      "multi-type asymmetric simple exclusion processes",
      "construction",
      "matrix product representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}