{
  "abstract": "We study the behavior at infinity of the invariant Radon measure for the multidimensional affine stochastic recursion $V_n = A_n V_{n-1} + B_n,$ where $(A_n)_{n \\geq 1}$ are positive random matrices, $(B_n)_{n \\geq 1}$ are random vectors with nonnegative entries, and $(A_n, B_n)_{n \\geq 1}$ are independent and identically distributed. In the critical regime where the top Lyapunov exponent of the random matrix products $A_n \\cdots A_1$ is zero, Brofferio, Peigné and Pham [6] recently established the existence and uniqueness, up to multiplication by a constant, of an invariant Radon measure with infinite total mass. They proved that the tail behavior of this measure when applied to radial sets is governed by a slowly varying function. Our goal is to show that this slowly varying function is actually bounded. Moreover, we investigate directional tail behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25944",
  "author_total": 3,
  "authors": [
    {
      "name": "Ion Grama"
    },
    {
      "name": "Sebastian Mentemeier"
    },
    {
      "name": "Hui Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dtgbd5njc2a4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25944",
  "fulltext_url": null,
  "id": "4dtgbd5njc2a4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25944",
  "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",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214104944",
  "pdf_url": "https://arxiv.org/pdf/2609.25944",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dtgbd5njc2a4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25944",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25944"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the tails of the invariant measure for multidimensional affine stochastic recursions in the critical case",
  "title_text": "On the tails of the invariant measure for multidimensional affine stochastic recursions in the critical case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/4dtgbd5njc2a4",
  "venue": "arXiv",
  "versions": []
}