{
  "id": "1112.0895",
  "version": "v2",
  "published": "2011-12-05T11:51:25.000Z",
  "updated": "2012-04-06T14:08:25.000Z",
  "title": "Markov Evolution of Continuum Particle Systems with Dispersion and Competition",
  "authors": [
    "Dmitri Finkelshtein",
    "Yuri Kondratiev",
    "Yuri Kozitsky",
    "Oleksandr Kutoviy"
  ],
  "comment": "43 pages",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We construct birth-and-death Markov evolution of states(distributions) of point particle systems in $\\mathbb{R}^d$. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other (compete). The main result is a statement that the corresponding correlation functions evolve in a scale of Banach spaces and remain sub-Poissonian, and hence no clustering occurs, if the dispersion is subordinate to the competition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-06T14:08:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92D25",
      "60J80",
      "82C22"
    ],
    "keywords": [
      "continuum particle systems",
      "dispersion",
      "competition",
      "construct birth-and-death markov evolution",
      "corresponding correlation functions evolve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0895F"
    }
  }
}