{
  "id": "1608.02161",
  "version": "v1",
  "published": "2016-08-06T22:57:13.000Z",
  "updated": "2016-08-06T22:57:13.000Z",
  "title": "Joint distributions of partial and global maxima of a Brownian Bridge",
  "authors": [
    "O. Benichou",
    "P. L. Krapivsky",
    "C. Mejia-Monasterio",
    "G. Oshanin"
  ],
  "comment": "13 pages, 7 figures",
  "journal": "J. Phys. A: Math. Theor. 49 335002 (2016)",
  "doi": "10.1088/1751-8113/49/33/335002",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We analyze the joint distributions and temporal correlations between the partial maximum $m$ and the global maximum $M$ achieved by a Brownian Bridge on the subinterval $[0,t_1]$ and on the entire interval $[0,t]$, respectively. We determine three probability distribution functions: The joint distribution $P(m,M)$ of both maxima; the distribution $P(m)$ of the partial maximum; and the distribution $\\Pi(G)$ of the gap between the maxima, $G = M-m$. We present exact results for the moments of these distributions and quantify the temporal correlations between $m$ and $M$ by calculating the Pearson correlation coefficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-06T22:57:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "joint distribution",
      "brownian bridge",
      "global maximum",
      "partial maximum",
      "temporal correlations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}