{
  "id": "1506.09030",
  "version": "v1",
  "published": "2015-06-30T11:04:27.000Z",
  "updated": "2015-06-30T11:04:27.000Z",
  "title": "Continuity and strict positivity of the multi-layer extension of the stochastic heat equation",
  "authors": [
    "Chin Hang Lun",
    "Jon Warren"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the continuity and strict positivity of the multi-layer extension to the stochastic heat equation introduced in [OW11] which form a hierarchy of partition functions for the continuum directed random polymer. This shows that the corresponding free energy (logarithm of the partition function) is well defined. This is also a step towards proving the conjecture stated at the end of the above paper that an array of such partition functions has the Markov property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-30T11:04:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic heat equation",
      "multi-layer extension",
      "strict positivity",
      "partition function",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150609030L"
    }
  }
}