{
  "id": "1607.07000",
  "version": "v1",
  "published": "2016-07-24T05:34:29.000Z",
  "updated": "2016-07-24T05:34:29.000Z",
  "title": "Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment",
  "authors": [
    "Firas Rassoul-Agha",
    "Timo Seppäläinen",
    "Atilla Yilmaz"
  ],
  "comment": "38 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the level-3 averaged and quenched large deviation principles from the point of view of the particle. In the averaged case the rate function is a specific relative entropy, while in the quenched case it is a Donsker-Varadhan type relative entropy for Markov processes. We relate these entropies to each other and seek to identify the minimizers of the level-3 to level-1 contractions in both settings. Motivation for this work comes from variational descriptions of the quenched free energy of directed polymer models where the same Markov process entropy appears.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-24T05:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F10",
      "82C41",
      "82C44"
    ],
    "keywords": [
      "dynamic random environment",
      "random walk",
      "markov process entropy appears",
      "rate function",
      "quenched large deviation principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}