{
  "annotation_id": "bee769ff-4426-4df1-8f35-d61924125fed",
  "date_created": "2026-02-17T05:53:20.185000Z",
  "date_modified": "2026-02-17T05:53:20.185000Z",
  "file_hash": "69ef9bf229d4022d9649e9ebe02f332a6450191e500f477644ccaab34dba448f",
  "private": false,
  "record": {
    "abstract": "Consider a unit-intensity point process $\\Pi$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $\\Pi$ and $V$ having small typical matching distances. When $\\Pi$ is either a Poisson process or i.i.d. perturbations of the vertex set, we determine the optimal matching distance and show that it can be attained by a factor matching scheme (that is, a deterministic and equivariant function of $\\Pi$).",
    "arxiv_id": "2601.08983",
    "authors": [
      "Yinon Spinka",
      "Oren Yakir"
    ],
    "categories": [
      "math.PR",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Optimal factor matchings for point processes on non-amenable unimodular graphs",
    "url": "https://arxiv.org/abs/2601.08983",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ef93003e-a82c-4fcd-859d-8bd36d1cfcf9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}