{
  "id": "2409.03324",
  "version": "v1",
  "published": "2024-09-05T07:53:06.000Z",
  "updated": "2024-09-05T07:53:06.000Z",
  "title": "Small gaps of GSE",
  "authors": [
    "Renjie Feng",
    "Jiaming Li",
    "Dong Yao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the smallest gaps for the Gaussian symplectic ensemble (GSE). We prove that the rescaled smallest gaps and their locations converge to a Poisson point process with an explicit rate. The approach provides an alternative proof for the GOE case and complements the results in \\cite{FTW}. By combining the main results from \\cite{BB, FTW, FW2}, the study of the smallest gaps for the classical random matrix ensembles C$\\beta$E and G$\\beta$E for $\\beta = 1, 2,$ and $4$ is now complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-05T07:53:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small gaps",
      "poisson point process",
      "classical random matrix ensembles",
      "gaussian symplectic",
      "explicit rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}