{
  "id": "1209.5882",
  "version": "v1",
  "published": "2012-09-26T09:27:27.000Z",
  "updated": "2012-09-26T09:27:27.000Z",
  "title": "Levy flights in confining environments: Random paths and their statistics",
  "authors": [
    "M. Zaba",
    "P. Garbaczewski",
    "V. Stephanovich"
  ],
  "comment": "10 pages, 7 figures",
  "journal": "Physica A 392 (17), 3485-3496, (2013)",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "physics.chem-ph",
    "physics.data-an"
  ],
  "abstract": "We analyze a specific class of random systems that are driven by a symmetric L\\'{e}vy stable noise. In view of the L\\'{e}vy noise sensitivity to the confining \"potential landscape\" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\\rho_*(x) \\sim \\exp [-\\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\\rho (x,t)$ dynamics directly from the random paths statistics. A priori given data are jump transition rates entering the master equation for $\\rho (x,t)$ and its target pdf $\\rho_*(x)$. We use numerical methods and construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. The generated sample trajectories show up a qualitative typicality, e.g. they display structural features of jumping paths (predominance of small vs large jumps) specific to particular stability indices $\\mu \\in (0,2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-26T09:27:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "levy flights",
      "confining environments",
      "pertinent random motion asymptotically sets",
      "probability density function",
      "random paths statistics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.physa.2013.04.028",
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2013,
      "month": "Sep",
      "volume": 392,
      "number": 17,
      "pages": 3485
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhyA..392.3485Z"
    }
  }
}