{
  "id": "1607.08804",
  "version": "v1",
  "published": "2016-07-29T13:37:27.000Z",
  "updated": "2016-07-29T13:37:27.000Z",
  "title": "Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions - Part II: Numerical Approach in Continuous Time",
  "authors": [
    "Esteban Guevara Hidalgo",
    "Takahiro Nemoto",
    "Vivien Lecomte"
  ],
  "comment": "12 pages, 11 figures. Second part of pair of companion papers, following Part I arXiv:1607.04752",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. Such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. In this second part of our study (which follows a companion paper [ arXiv:1607.04752 ] dedicated to an analytical study), we present a numerical approach which verifies and uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. Using the continuous-time cloning algorithm, we propose a method aimed at extracting the infinite-time and infinite-size limits of the estimator of such large deviation functions in a simple system, where, by comparing the numerical results to exact analytical ones, we demonstrate the practical efficiency of our proposed approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T13:37:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation functions",
      "numerical approach",
      "size scalings",
      "continuous time",
      "rare trajectories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}