{
  "id": "2312.12348",
  "version": "v1",
  "published": "2023-12-19T17:28:43.000Z",
  "updated": "2023-12-19T17:28:43.000Z",
  "title": "An ergodic theorem with weights and applications to random measures, homogenization and hydrodynamics",
  "authors": [
    "A. Faggionato"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We prove a multidimensional ergodic theorem with weighted averages for the action of the group $\\mathbb{Z}^d$ on a probability space. At level $n$ weights are of the form $n^{-d} \\psi(j/n)$, $ j\\in \\mathbb{Z}^d$, for real functions $\\psi$ decaying suitably fast. We discuss applications to random measures and to quenched stochastic homogenization of random walks on simple point processes with long-range random jump rates, allowing to remove the technical Assumption (A9) from \\cite[Theorem~4.4]{Fhom1}. This last result concerns also some semigroup and resolvent convergence particularly relevant for the derivation of the quenched hydrodynamic limit of interacting particle systems via homogenization and duality. As a consequence we show that also the quenched hydrodynamic limit of the symmetric simple exclusion process on point processes stated in \\cite[Theorem~4.1]{F_SEP} remains valid when removing the above mentioned Assumption (A9).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-19T17:28:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "60G55",
      "60K37",
      "35B27"
    ],
    "keywords": [
      "random measures",
      "applications",
      "quenched hydrodynamic limit",
      "long-range random jump rates",
      "symmetric simple exclusion process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}