{
  "id": "1012.3140",
  "version": "v1",
  "published": "2010-12-14T19:24:07.000Z",
  "updated": "2010-12-14T19:24:07.000Z",
  "title": "Time scales in large systems of Brownian particles with stochastic synchronization",
  "authors": [
    "Anatoly Manita"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\\{\\tau_{n}\\}_{n=1}^{\\infty}$. Under assumption that the free Brownian motions and the sequence $\\{\\tau_{n}\\}_{n=1}^{\\infty}$ are independent we study asymptotic properties of the system when both the dimension~$N$ and the time~$t$ go to infinity. We find three time scales $t=t(N)$ of qualitatively different behavior of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-14T19:24:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J27"
    ],
    "keywords": [
      "brownian particles",
      "time scales",
      "large systems",
      "stochastic synchronization",
      "random time moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3140M"
    }
  }
}