{
  "id": "1701.08400",
  "version": "v1",
  "published": "2017-01-29T16:49:46.000Z",
  "updated": "2017-01-29T16:49:46.000Z",
  "title": "Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem",
  "authors": [
    "Thomas S. Jacq",
    "Carlos F. Lardizabal"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative instance of the gambler's ruin is studied, expressions for the probability of reaching a certain fortune and the mean time to reach a fortune or ruin are described via a counting technique for boundary restricted paths in a lattice, due to Kobayashi et al. We also discuss an open quantum version of Foster's Theorem for the expected return time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-29T16:49:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open quantum random walks",
      "fosters theorem",
      "karlin-mcgregor formula",
      "path counting",
      "open quantum version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}