{
  "id": "math/0608540",
  "version": "v1",
  "published": "2006-08-22T12:08:09.000Z",
  "updated": "2006-08-22T12:08:09.000Z",
  "title": "Growth and roughness of the interface for ballistic deposition",
  "authors": [
    "Mathew D. Penrose"
  ],
  "comment": "26 pages. 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In ballistic deposition (BD), $(d+1)$-dimensional particles fall sequentially at random towards an initially flat, large but bounded $d$-dimensional surface, and each particle sticks to the first point of contact. For both lattice and continuum BD, a law of large numbers in the thermodynamic limit establishes convergence of the mean height and surface width of the interface to constants $h(t)$ and $w(t)$, respectively, depending on time $t$. We show that $h(t)$ is asymptotically linear in $t$, while $w(t)$ grows at least logarithmically in $t$ when $d=1$. We also give duality results saying that the height above the origin for deposition onto an initially flat surface is equidistributed with the maximum height for deposition onto a surface growing from a single site.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-22T12:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "60D05",
      "60E15"
    ],
    "keywords": [
      "ballistic deposition",
      "thermodynamic limit establishes convergence",
      "initially flat",
      "dimensional surface",
      "particle sticks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8540P"
    }
  }
}