{
  "abstract": "We prove a dimension-free Markov--Bernstein-type inequality for polynomial mappings $(f_1,f_2)\\colon\\mathbb R^n\\to\\mathbb R^2$ of degree at most $d$. For product probability measures whose one-dimensional marginals have densities bounded by $1$, we obtain a lower bound for the integral of the Gram determinant of $\\nabla f_1$ and $\\nabla f_2$ in terms of the Gram determinant of the $d$-th derivative tensors $D^df_1$ and $D^df_2$, with a constant depending only on $d$. For pairs in a fixed Wiener chaos, the resulting Gaussian inequality answers a question of Nourdin, Nualart, and Poly concerning a lower bound for the expectation of the Malliavin determinant in terms of the determinant of the covariance matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13836",
  "author_total": 1,
  "authors": [
    {
      "name": "Egor Kosov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/39byr6gdz3wed.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13836",
  "fulltext_url": null,
  "id": "39byr6gdz3wed",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13836",
  "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.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7221531757",
  "pdf_url": "https://arxiv.org/pdf/2610.13836",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/39byr6gdz3wed.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13836",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13836"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Dimension-free Markov--Bernstein-type inequality for $\\mathbb R^2$-valued polynomials",
  "title_text": "Dimension-free Markov--Bernstein-type inequality for ℝ^2-valued polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/39byr6gdz3wed",
  "venue": "arXiv",
  "versions": []
}