{
  "id": "1810.03580",
  "version": "v1",
  "published": "2018-10-08T17:03:10.000Z",
  "updated": "2018-10-08T17:03:10.000Z",
  "title": "Busemann functions and Gibbs measures in directed polymer models on $\\mathbb{Z}^2$",
  "authors": [
    "Christopher Janjigian",
    "Firas Rassoul-Agha"
  ],
  "comment": "48 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planer square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/non-uniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin-Lanford-Ruelle equations). We also prove non-existence of covariant or deterministically directed bi-infinite polymer measures. Along the way, we prove almost sure existence of Busemann function limits in directions where the limiting free energy has some regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-08T17:03:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "directed polymer models",
      "gibbs measures",
      "space-time random potential",
      "busemann function limits",
      "planer square lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}