{
  "id": "cond-mat/9810136",
  "version": "v2",
  "published": "1998-10-12T15:33:59.000Z",
  "updated": "1998-12-02T17:46:51.000Z",
  "title": "Analytical results for random walk persistence",
  "authors": [
    "Clement Sire",
    "Satya N. Majumdar",
    "Andreas Rudinger"
  ],
  "comment": "23 pages; accepted for publication to Phys. Rev. E (Dec. 98)",
  "journal": "Phys. Rev. E 61, 1258 (2000)",
  "doi": "10.1103/PhysRevE.61.1258",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In this paper, we present the detailed calculation of the persistence exponent $\\theta$ for a nearly-Markovian Gaussian process $X(t)$, a problem initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. New resummed perturbative and non-perturbative expressions for $\\theta$ are obtained, which suggest a connection with the result of the alternative independent interval approximation (IIA). The perturbation theory is extended to the calculation of $\\theta$ for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and non-perturbative expressions for the persistence exponent $\\theta(X_0)$, describing the probability that the process remains bigger than $X_0\\sqrt{<X^2(t)>}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-12-02T17:46:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walk persistence",
      "analytical results",
      "persistence exponent",
      "process remains bigger",
      "nearly-markovian gaussian process"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}