{
  "id": "0804.1810",
  "version": "v2",
  "published": "2008-04-10T21:36:22.000Z",
  "updated": "2016-09-10T01:04:03.000Z",
  "title": "Last Passage Percolation in Macroscopically Inhomogeneous Media",
  "authors": [
    "Leonardo T. Rolla",
    "Augusto Q. Teixeira"
  ],
  "journal": "Electronic Communications in Probability, v. 13, p. 131-139, 2008",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniqueness of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-10T21:36:22.000Z",
      "comment": "8 pages, 2 figures",
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-09-10T01:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82D60",
      "60F10"
    ],
    "keywords": [
      "macroscopically inhomogeneous media",
      "variational problem",
      "totally asymmetric simple exclusion process",
      "passage percolation model",
      "passage time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1810R"
    }
  }
}