{
  "abstract": "Schultz [Comm.~Pure~Appl.~Math., 1998] first established dispersive estimates for the fundamental solution of the discrete wave equation on lattice graphs $\\Z^d$ for $d=2,3$, which can be seen as a discrete analogue of the classical dispersive estimate for the Euclidean wave equation. His result was extended by Bi, Cheng and Hua to $d=4$ and $5$. In this paper, we give complete answers to all the remaining dimensions, including $d=5$. Our estimate is sharp for every $d\\geq 5$. Moreover, the proof remains valid for the upper bound of the case for $d=4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05930",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhe You"
    },
    {
      "name": "Xiongfeng Zhan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mykfd22bs690.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05930",
  "fulltext_url": null,
  "id": "8mykfd22bs690",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05930",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212048310",
  "pdf_url": "https://arxiv.org/pdf/2609.05930",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mykfd22bs690.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05930",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05930"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp dispersive estimates for wave equation on lattice graphs with high dimension",
  "title_text": "Sharp dispersive estimates for wave equation on lattice graphs with high dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8mykfd22bs690",
  "venue": "arXiv",
  "versions": []
}