{
  "abstract": "A max filter with Gaussian templates $a_1,\\dots,a_D$ is a $G$-invariant map $\\R^d\\to\\R^D$, where $G$ is a finite reflection group. As $D\\to\\infty$ its distortion converges a.s to the condition number of $M_G^{1/2}$, where $M_G$ is the second-moment matrix of a standard Gaussian vector moved into a fundamental chamber of $G$. We compute this limit exactly for the sign and dihedral groups, and show it grows as $Θ(\\sqrt d)$, $Θ(d^{3/2})$ and $Θ(k)$ for the sign, symmetric and dihedral groups of order $2k$. The symmetric case bound uses a lower bound on the covariance of order statistics. For any finite $G$ we also show that the infimum defining the optimal lower Lipschitz constant of a piecewise-linear $G$-invariant map is a minimum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00305",
  "author_total": 1,
  "authors": [
    {
      "name": "Efstratios Tsoukanis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7emqw21mft1m0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00305",
  "fulltext_url": null,
  "id": "7emqw21mft1m0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00305",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7emqw21mft1m0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Distortion of Random Max Filters over Reflection Groups",
  "title_text": "Distortion of Random Max Filters over Reflection Groups",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7emqw21mft1m0",
  "venue": "arXiv",
  "versions": []
}