{
  "id": "1607.04752",
  "version": "v1",
  "published": "2016-07-16T15:37:36.000Z",
  "updated": "2016-07-16T15:37:36.000Z",
  "title": "Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions - Part I: Analytical Study using a Birth-Death Process",
  "authors": [
    "Takahiro Nemoto",
    "Esteban Guevara Hidalgo",
    "Vivien Lecomte"
  ],
  "comment": "Part 1/2",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The Giardin\\`a-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time-evolution of the population-probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a simple two-state model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-16T15:37:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation functions",
      "size scalings",
      "analytical study",
      "finite-time",
      "evaluation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}