{
  "abstract": "Let $G$ be a locally compact group, let $Γ$ be a lattice in $G$, and let $η$ be a spread-out probability measure on $G$. A Furstenberg discretization of $η$ to $Γ$ is a probability measure $μ$ on $Γ$ such that every $(G,η)$-stationary space is also $(Γ,μ)$-stationary. For cocompact lattices $Γ$ and under mild regularity conditions on $η$, we construct Furstenberg discretizations satisfying finite moment conditions of arbitrary order with respect to arbitrary prescribed subadditive functions. Our approach relies on a rather general study of differential entropy and Lyapunov exponents in the setting of locally compact groups. We relate Lyapunov exponents to spectral radii in weighted $L^{1}$-algebras and prove vanishing results for weights coming from length functions. Additionally, we prove that if $G$ has the property of rapid decay or the Kunze--Stein property, this yields entropy formulas for stationary actions whose Koopman representation is weakly contained in the left-regular representation. As consequences, we obtain preservation results for Poisson boundaries under discretization and characterize Zimmer amenability of stationary actions in terms of weak containment and maximal Furstenberg entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12268",
  "author_total": 4,
  "authors": [
    {
      "name": "Benjamin Anderson-Sackaney"
    },
    {
      "name": "Tim de Laat"
    },
    {
      "name": "Ebrahim Samei"
    },
    {
      "name": "Matthew Wiersma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgezr56j9nnjj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12268",
  "fulltext_url": null,
  "id": "dgezr56j9nnjj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12268",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221134703",
  "pdf_url": "https://arxiv.org/pdf/2610.12268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgezr56j9nnjj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Furstenberg discretization with moment control and entropy rigidity",
  "title_text": "Furstenberg discretization with moment control and entropy rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/dgezr56j9nnjj",
  "venue": "arXiv",
  "versions": []
}