{
  "abstract": "We present self-contained martingale proofs of Talagrand's convolution conjecture in the Gaussian and Boolean settings with explicit dimension-free constants. The argument is based on the analysis of the stopped density martingale and a weighted Itô isometry estimate. The Gaussian case was settled by Eldan and Lee, and Lehec; the Boolean case was proved up to a $\\log\\log$ factor by Chen and recently settled by Lu, Guo and Fang.",
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  "article_type": null,
  "arxiv": "2609.11290",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Shaposhnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cyqvr8mhsza81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11290",
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  "native_subjects": [
    [
      "arxiv",
      "math.FA"
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      "math.PR"
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      "openalex",
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  "pdf_url": "https://arxiv.org/pdf/2609.11290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cyqvr8mhsza81.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.11290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11290"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
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  "title": "Some remarks on Talagrand's convolution conjecture",
  "title_text": "Some remarks on Talagrand's convolution conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/cyqvr8mhsza81",
  "venue": "arXiv",
  "versions": []
}