{
  "abstract": "Let $C_1,\\ldots,C_k$ be the convex hulls of independent partial-sum processes in $\\mathbb{R}^d$ whose increments are exchangeable within each process. We express the expected mixed volume $\\mathbb{E} V_d(C_1[m_1],\\ldots,C_k[m_k])$, $m_1+\\cdots+m_k=d$, through mean absolute determinants of disjoint block sums of the increments; no general-position assumption is needed. For random walks with i.i.d. integrable increments the block sums are independent, and the formula extends the expected-volume formula of Barndorff-Nielsen and Baxter and of Vysotsky and Zaporozhets to mixed volumes. We then prove a continuous-time counterpart: for independent Lévy processes with finite first moments, the expected mixed volume of the closed convex hulls of their paths is an explicit integral of mean absolute determinants over a product of simplices. For symmetric stable processes the integral is evaluated in terms of the associated zonoids. As a geometric application, we compute the mean mixed volume of random projections of mutually orthogonal canonical orthoschemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10228",
  "author_total": 2,
  "authors": [
    {
      "name": "Artyom Bolotin"
    },
    {
      "name": "Dmitry Zaporozhets"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/720j9940tc89d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10228",
  "fulltext_url": null,
  "id": "720j9940tc89d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10228",
  "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"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7220906346",
  "pdf_url": "https://arxiv.org/pdf/2610.10228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/720j9940tc89d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Expected mixed volumes of convex hulls of random walks and Lévy processes",
  "title_text": "Expected mixed volumes of convex hulls of random walks and Lévy processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/720j9940tc89d",
  "venue": "arXiv",
  "versions": []
}