{
  "id": "1706.05564",
  "version": "v1",
  "published": "2017-06-17T17:16:00.000Z",
  "updated": "2017-06-17T17:16:00.000Z",
  "title": "An invariance principle for the stochastic heat equation",
  "authors": [
    "Mathew Joseph"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d. mean zero random variables. As a consequence, we give an alternative proof of the weak convergence of the scaled partition function of directed polymers in the intermediate disorder regime, to the stochastic heat equation; an advantage of the proof is that it gives the convergence of all moments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-17T17:16:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60F05",
      "60K35"
    ],
    "keywords": [
      "invariance principle",
      "white-noise driven stochastic heat equation",
      "mean zero random variables",
      "discrete time random walk",
      "intermediate disorder regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}