{
  "id": "2310.07640",
  "version": "v1",
  "published": "2023-10-11T16:37:51.000Z",
  "updated": "2023-10-11T16:37:51.000Z",
  "title": "Gaussian deconvolution and the lace expansion for spread-out models",
  "authors": [
    "Yucheng Liu",
    "Gordon Slade"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a new proof of $|x|^{-(d-2)}$ decay of critical two-point functions for spread-out statistical mechanical models on $\\mathbb{Z}^d$ above the upper critical dimension, based on the lace expansion and assuming appropriate diagrammatic estimates. Applications include spread-out models of the Ising model and self-avoiding walk in dimensions $d>4$, and spread-out percolation for $d>6$. The proof is based on an extension of the new Gaussian deconvolution theorem we obtained in a recent paper. It provides a technically simpler and conceptually more transparent approach than the method of Hara, van der Hofstad and Slade (2003).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-11T16:37:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05",
      "60K35",
      "82B27",
      "82B41",
      "82B43"
    ],
    "keywords": [
      "lace expansion",
      "spread-out models",
      "assuming appropriate diagrammatic estimates",
      "gaussian deconvolution theorem",
      "van der hofstad"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}