{
  "annotation_id": "d9d745ef-fa42-40cd-a35b-d82c6f801196",
  "date_created": "2026-02-17T05:53:19.905000Z",
  "date_modified": "2026-02-17T05:53:19.905000Z",
  "file_hash": "06eb0f6f4feebb2baa4d1c67d6dbc31d85c193313a941475090e31b846c60c4e",
  "private": false,
  "record": {
    "abstract": "In this paper, we establish a connection between the formalism of $\\mathcal{R}$-transforms for non-Hermitian random matrices and the framework of spherical integrals, using the replica method. This connection was previously proved in the Hermitian setting and in the case of bi-invariant random matrices. We show that the $\\mathcal{R}$-transforms used in the non-Hermitian context in fact originate from a single scalar function of two variables. This provides a new and transparent way to compute $\\mathcal{R}$-transforms, which until now had been known only in restricted cases such as bi-invariant, Hermitian, or elliptic ensembles.",
    "arxiv_id": "2601.09360",
    "authors": [
      "Pierre Bousseyroux",
      "Marc Potters"
    ],
    "categories": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "$\\mathcal{R}$-transforms for Non-Hermitian Matrices: A Spherical Integral Approach",
    "url": "https://arxiv.org/abs/2601.09360",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e8d16317-39ce-497d-9baa-dc75585bf464",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}