{
  "id": "1412.8678",
  "version": "v1",
  "published": "2014-12-30T16:44:40.000Z",
  "updated": "2014-12-30T16:44:40.000Z",
  "title": "Strong Markov property of determinantal processes with extended kernels",
  "authors": [
    "Hirofumi Osada",
    "Hideki Tanemura"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Noncolliding Brownian motion (Dyson's Brownian motion model with parameter $\\beta=2$) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scaling limits, these processes converge to determinantal processes describing systems with an infinite number of particles. The main purpose of this paper is to show the strong Markov property of these limit processes, which are determinantal processes with the extended sine kernel, extended Airy kernel and extended Bessel kernel, respectively. We also determine the quasi-regular Dirichlet forms and stochastic differential equations associated with the processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-30T16:44:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "30C15",
      "47D07",
      "60G55",
      "82C22"
    ],
    "keywords": [
      "strong markov property",
      "extended kernels",
      "dysons brownian motion model",
      "stochastic differential equations",
      "quasi-regular dirichlet forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8678O"
    }
  }
}