{
  "id": "cond-mat/0406388",
  "version": "v1",
  "published": "2004-06-17T09:13:49.000Z",
  "updated": "2004-06-17T09:13:49.000Z",
  "title": "Random walk and trapping processes on scale-free networks",
  "authors": [
    "Lazaros K. Gallos"
  ],
  "comment": "8 pages, 5 figures",
  "journal": "Phys. Rev. E, 70, 046116 (2004).",
  "doi": "10.1103/PhysRevE.70.046116",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the survival probability on a network with a concentration $c$ of static traps. We show that the random walkers remain close to their origin, but cover a large part of the network at the same time. This behavior is markedly different than usual random walk processes in the literature. For the trapping problem we numerically compute $\\Phi(n,c)$, the survival probability of mobile species at time $n$, as a function of the concentration of trap nodes, $c$. Comparison of our results to the Rosenstock approximation indicate that this is an adequate description for networks with $2<\\gamma<3$ and yield an exponential decay. For $\\gamma>3$ the behavior is more complicated and one needs to employ a truncated cumulant expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-17T09:13:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scale-free networks",
      "trapping processes",
      "random walkers remain close",
      "survival probability",
      "usual random walk processes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}