{
  "id": "1810.04212",
  "version": "v1",
  "published": "2018-10-09T18:52:36.000Z",
  "updated": "2018-10-09T18:52:36.000Z",
  "title": "Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise",
  "authors": [
    "Prakash Chakraborty",
    "Xia Chen",
    "Bo Gao",
    "Samy Tindel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $\\dot{W}$ in space. We consider the case $H<\\frac{1}{2}$ and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form $\\frac{1}{2} \\Delta + \\dot{W}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T18:52:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic heat equation driven",
      "rough spatial noise",
      "quenched asymptotics",
      "parabolic anderson model",
      "time-independent fractional noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}