{
  "id": "1810.03850",
  "version": "v1",
  "published": "2018-10-09T08:25:20.000Z",
  "updated": "2018-10-09T08:25:20.000Z",
  "title": "Sharp convergence of nonlinear functionals of a class of Gaussian random fields",
  "authors": [
    "Weijun Xu"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in [Hairer-Xu], but with improved estimates. As a consequence, we establish convergence of a class of Gaussian fields composite with more general functions. These bounds and convergences are useful ingredients to establish weak universalities of several singular stochastic PDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T08:25:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian random fields",
      "nonlinear functionals",
      "sharp convergence",
      "singular stochastic pdes",
      "gaussian fields composite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}