{
  "abstract": "We consider the $Φ^4_d$ measure under radial symmetry on the unit ball, formally given by $$dρ(u) = \\frac 1 Z \\exp\\Big( - \\frac 14 \\int_{B_1} |u|^4 dx - \\frac 12 \\int_{B_1} |\\nabla u|^2 dx\\Big) d u, $$ where $u$ is restricted to radially symmetric functions with 0 boundary conditions. We prove that for every dimension $d$, there exists such a measure, which is concentrated on $L^p(B_1)$ for every $p < \\frac{2d}{d-2}$ (for every $p < \\infty$ if $d \\le 2$). Furthermore, we show that these measures are not Gaussian, and when $d \\ge 4$, they are singular with respect to the underlying Gaussian measure. We achieve this result by first defining the measure $ρ^+_δ[λ]$ on the shell $\\{δ\\le |x| \\le 1\\}$, $0 < δ< 1$, with a boundary condition on the sphere of radius $δ$ of the form $u|_{\\{|x| = δ\\}} = λ$. Then we prove that this measure satisfies a variational formula, and use it to show moment bounds which are uniform in the boundary value $λ$. A crucial ingredient in this argument is the fact that every solution of the elliptic equation $-Δu + u^3 = 0$ on the annulus $\\{ δ\\le |x| \\le 1 \\}$ satisfies uniform bounds inside the domain, independently of the boundary conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31267",
  "author_total": 4,
  "authors": [
    {
      "name": "Tadahiro Oh"
    },
    {
      "name": "Leonardo Tolomeo"
    },
    {
      "name": "Nikolay Tzvetkov"
    },
    {
      "name": "Yuzhao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dtyc060dqfwwg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31267",
  "fulltext_url": null,
  "id": "dtyc060dqfwwg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31267",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223294910",
  "pdf_url": "https://arxiv.org/pdf/2610.31267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dtyc060dqfwwg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31267"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Radial $Φ^4$ models in supercritical regimes",
  "title_text": "Radial Φ^4 models in supercritical regimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/dtyc060dqfwwg",
  "venue": "arXiv",
  "versions": []
}