{
  "id": "2211.14472",
  "version": "v1",
  "published": "2022-11-26T04:08:17.000Z",
  "updated": "2022-11-26T04:08:17.000Z",
  "title": "A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold",
  "authors": [
    "Satoshi Ishiwata",
    "Hiroshi Kawabi"
  ],
  "categories": [
    "math.FA",
    "math.DG",
    "math.PR"
  ],
  "abstract": "In the present paper, we prove that the contraction $C_{0}$-semigroup generated by a Schr\\\"odinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also obtain a quantitative error estimate of the convergence. Finally, we give examples of the partition of the manifold and the drift term on two typical manifolds: Euclidean spaces and model manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-26T04:08:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D08",
      "58J65",
      "05C81"
    ],
    "keywords": [
      "complete riemannian manifold",
      "graph discretized approximation",
      "discrete time random walks",
      "model manifolds",
      "euclidean spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}