{
  "id": "1403.6353",
  "version": "v1",
  "published": "2014-03-25T14:18:02.000Z",
  "updated": "2014-03-25T14:18:02.000Z",
  "title": "Singular stochastic PDEs",
  "authors": [
    "Martin Hairer"
  ],
  "comment": "Proceedings of the ICM",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This problem can be addressed within the framework of the recently developed theory of \"regularity structures\", which allows to describe candidate solutions locally by a \"jet\", but where the usual Taylor polynomials are replaced by a sequence of custom-built objects. In order to illustrate the theory, we focus on the particular example of the Kardar-Parisi-Zhang equation, a popular model for interface propagation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-25T14:18:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "81S20",
      "82C28"
    ],
    "keywords": [
      "singular stochastic pdes",
      "singular parabolic stochastic partial differential",
      "parabolic stochastic partial differential equations",
      "usual taylor polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.6353H"
    }
  }
}