{
  "id": "2502.09493",
  "version": "v1",
  "published": "2025-02-13T16:59:36.000Z",
  "updated": "2025-02-13T16:59:36.000Z",
  "title": "Quantitative estimates for high-contrast random media",
  "authors": [
    "Peter Bella",
    "Matteo Capoferri",
    "Mikhail Cherdantsev",
    "Igor Velčić"
  ],
  "comment": "42 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "This paper studies quantitative homogenization of elliptic equations with random, uniformly elliptic coefficients that vanish in a union of random holes. Assuming an upper bound on the size of the holes and a separation condition between them, we derive optimal bounds for the regularity radius $r_*$ and suboptimal growth estimates for the corrector. These results are key ingredients for error analysis in stochastic homogenization and serve as crucial input for recent developments in the double-porosity model, such as those by Bonhomme, Duerinckx, and Gloria (https://arxiv.org/abs/2502.02847).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-13T16:59:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "60H25",
      "35B27",
      "35B40",
      "74A40",
      "74Q05"
    ],
    "keywords": [
      "high-contrast random media",
      "quantitative estimates",
      "paper studies quantitative homogenization",
      "suboptimal growth estimates",
      "elliptic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}